326.38/101.18 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml

326.38/101.18

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The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^1)).

0 CpxTRS

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↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))

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↳2 CdtProblem

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↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳4 CdtProblem

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↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))

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↳6 CdtProblem

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↳7 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳8 CdtProblem

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↳9 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳10 CdtProblem

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↳11 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳12 CdtProblem

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↳13 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳14 CdtProblem

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↳15 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳16 CdtProblem

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↳17 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳18 CdtProblem

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↳19 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))

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↳20 CdtProblem

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↳21 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳22 CdtProblem

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↳23 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳24 CdtProblem

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↳25 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))

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↳26 CdtProblem

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↳27 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳28 CdtProblem

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↳29 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳30 CdtProblem

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↳31 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳32 CdtProblem

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↳33 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳34 CdtProblem

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↳35 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳36 CdtProblem

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↳37 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳38 CdtProblem

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↳39 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳40 CdtProblem

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↳41 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳42 CdtProblem

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↳43 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳44 CdtProblem

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↳45 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳46 CdtProblem

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↳47 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳48 CdtProblem

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↳49 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳50 CdtProblem

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↳51 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳52 CdtProblem

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↳53 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳54 CdtProblem

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↳55 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳56 CdtProblem

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↳57 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳58 CdtProblem

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↳59 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳60 CdtProblem

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↳61 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳62 CdtProblem

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↳63 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳64 CdtProblem

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↳65 CdtUnreachableProof (⇔)

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↳66 CdtProblem

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↳67 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳68 CdtProblem

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↳69 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))

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↳70 CdtProblem

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↳71 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳72 CdtProblem

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↳73 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳74 CdtProblem

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↳75 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳76 CdtProblem

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↳77 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳78 CdtProblem

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↳79 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳80 CdtProblem

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↳81 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳82 CdtProblem

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↳83 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳84 CdtProblem

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↳85 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳86 CdtProblem

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↳87 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳88 CdtProblem

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↳89 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳90 CdtProblem

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↳91 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳92 CdtProblem

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↳93 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))

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↳94 CdtProblem

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↳95 SIsEmptyProof (BOTH BOUNDS(ID, ID))

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↳96 BOUNDS(O(1), O(1))

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(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following rules:

active(terms(N)) → mark(cons(recip(sqr(N)), terms(s(N)))) 326.74/101.22
active(sqr(0)) → mark(0) 326.74/101.22
active(sqr(s(X))) → mark(s(add(sqr(X), dbl(X)))) 326.74/101.22
active(dbl(0)) → mark(0) 326.74/101.22
active(dbl(s(X))) → mark(s(s(dbl(X)))) 326.74/101.22
active(add(0, X)) → mark(X) 326.74/101.22
active(add(s(X), Y)) → mark(s(add(X, Y))) 326.74/101.22
active(first(0, X)) → mark(nil) 326.74/101.22
active(first(s(X), cons(Y, Z))) → mark(cons(Y, first(X, Z))) 326.74/101.22
active(terms(X)) → terms(active(X)) 326.74/101.22
active(cons(X1, X2)) → cons(active(X1), X2) 326.74/101.22
active(recip(X)) → recip(active(X)) 326.74/101.22
active(sqr(X)) → sqr(active(X)) 326.74/101.22
active(add(X1, X2)) → add(active(X1), X2) 326.74/101.22
active(add(X1, X2)) → add(X1, active(X2)) 326.74/101.22
active(dbl(X)) → dbl(active(X)) 326.74/101.22
active(first(X1, X2)) → first(active(X1), X2) 326.74/101.22
active(first(X1, X2)) → first(X1, active(X2)) 326.74/101.22
terms(mark(X)) → mark(terms(X)) 326.74/101.22
cons(mark(X1), X2) → mark(cons(X1, X2)) 326.74/101.22
recip(mark(X)) → mark(recip(X)) 326.74/101.22
sqr(mark(X)) → mark(sqr(X)) 326.74/101.22
add(mark(X1), X2) → mark(add(X1, X2)) 326.74/101.22
add(X1, mark(X2)) → mark(add(X1, X2)) 326.74/101.22
dbl(mark(X)) → mark(dbl(X)) 326.74/101.22
first(mark(X1), X2) → mark(first(X1, X2)) 326.74/101.22
first(X1, mark(X2)) → mark(first(X1, X2)) 326.74/101.22
proper(terms(X)) → terms(proper(X)) 326.74/101.22
proper(cons(X1, X2)) → cons(proper(X1), proper(X2)) 326.74/101.22
proper(recip(X)) → recip(proper(X)) 326.74/101.22
proper(sqr(X)) → sqr(proper(X)) 326.74/101.22
proper(s(X)) → s(proper(X)) 326.74/101.22
proper(0) → ok(0) 326.74/101.22
proper(add(X1, X2)) → add(proper(X1), proper(X2)) 326.74/101.22
proper(dbl(X)) → dbl(proper(X)) 326.74/101.22
proper(first(X1, X2)) → first(proper(X1), proper(X2)) 326.74/101.22
proper(nil) → ok(nil) 326.74/101.22
terms(ok(X)) → ok(terms(X)) 326.74/101.22
cons(ok(X1), ok(X2)) → ok(cons(X1, X2)) 326.74/101.22
recip(ok(X)) → ok(recip(X)) 326.74/101.22
sqr(ok(X)) → ok(sqr(X)) 326.74/101.22
s(ok(X)) → ok(s(X)) 326.74/101.22
add(ok(X1), ok(X2)) → ok(add(X1, X2)) 326.74/101.22
dbl(ok(X)) → ok(dbl(X)) 326.74/101.22
first(ok(X1), ok(X2)) → ok(first(X1, X2)) 326.74/101.22
top(mark(X)) → top(proper(X)) 326.74/101.22
top(ok(X)) → top(active(X))

Rewrite Strategy: INNERMOST

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(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted CpxTRS to CDT

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(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 326.74/101.22
active(sqr(0)) → mark(0) 326.74/101.22
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 326.74/101.22
active(dbl(0)) → mark(0) 326.74/101.22
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 326.74/101.22
active(add(0, z0)) → mark(z0) 326.74/101.22
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 326.74/101.22
active(first(0, z0)) → mark(nil) 326.74/101.22
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 326.74/101.22
active(terms(z0)) → terms(active(z0)) 326.74/101.22
active(cons(z0, z1)) → cons(active(z0), z1) 326.74/101.22
active(recip(z0)) → recip(active(z0)) 326.74/101.22
active(sqr(z0)) → sqr(active(z0)) 326.74/101.22
active(add(z0, z1)) → add(active(z0), z1) 326.74/101.22
active(add(z0, z1)) → add(z0, active(z1)) 326.74/101.22
active(dbl(z0)) → dbl(active(z0)) 326.74/101.22
active(first(z0, z1)) → first(active(z0), z1) 326.74/101.22
active(first(z0, z1)) → first(z0, active(z1)) 326.74/101.22
terms(mark(z0)) → mark(terms(z0)) 326.74/101.22
terms(ok(z0)) → ok(terms(z0)) 326.74/101.22
cons(mark(z0), z1) → mark(cons(z0, z1)) 326.74/101.22
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 326.74/101.22
recip(mark(z0)) → mark(recip(z0)) 326.74/101.22
recip(ok(z0)) → ok(recip(z0)) 326.74/101.22
sqr(mark(z0)) → mark(sqr(z0)) 326.74/101.22
sqr(ok(z0)) → ok(sqr(z0)) 326.74/101.22
add(mark(z0), z1) → mark(add(z0, z1)) 326.74/101.22
add(z0, mark(z1)) → mark(add(z0, z1)) 326.74/101.22
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 326.74/101.22
dbl(mark(z0)) → mark(dbl(z0)) 326.74/101.22
dbl(ok(z0)) → ok(dbl(z0)) 326.74/101.22
first(mark(z0), z1) → mark(first(z0, z1)) 326.74/101.22
first(z0, mark(z1)) → mark(first(z0, z1)) 326.74/101.22
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 326.74/101.22
proper(terms(z0)) → terms(proper(z0)) 326.74/101.22
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 326.74/101.22
proper(recip(z0)) → recip(proper(z0)) 326.74/101.22
proper(sqr(z0)) → sqr(proper(z0)) 326.74/101.22
proper(s(z0)) → s(proper(z0)) 326.74/101.22
proper(0) → ok(0) 326.74/101.22
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 326.74/101.22
proper(dbl(z0)) → dbl(proper(z0)) 326.74/101.22
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 326.74/101.22
proper(nil) → ok(nil) 326.74/101.22
s(ok(z0)) → ok(s(z0)) 326.74/101.22
top(mark(z0)) → top(proper(z0)) 326.74/101.22
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(terms(z0)) → c(CONS(recip(sqr(z0)), terms(s(z0))), RECIP(sqr(z0)), SQR(z0), TERMS(s(z0)), S(z0)) 326.74/101.22
ACTIVE(sqr(s(z0))) → c2(S(add(sqr(z0), dbl(z0))), ADD(sqr(z0), dbl(z0)), SQR(z0), DBL(z0)) 326.74/101.22
ACTIVE(dbl(s(z0))) → c4(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 326.74/101.22
ACTIVE(add(s(z0), z1)) → c6(S(add(z0, z1)), ADD(z0, z1)) 326.74/101.22
ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2)) 326.74/101.22
ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.22
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.22
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.22
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.22
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.22
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.22
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.22
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.22
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.22
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.22
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.22
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.22
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.22
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.22
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.22
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.22
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.22
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.22
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.22
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.22
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.22
S(ok(z0)) → c44(S(z0)) 326.74/101.22
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 326.74/101.22
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0))

S tuples:

ACTIVE(terms(z0)) → c(CONS(recip(sqr(z0)), terms(s(z0))), RECIP(sqr(z0)), SQR(z0), TERMS(s(z0)), S(z0)) 326.74/101.22
ACTIVE(sqr(s(z0))) → c2(S(add(sqr(z0), dbl(z0))), ADD(sqr(z0), dbl(z0)), SQR(z0), DBL(z0)) 326.74/101.22
ACTIVE(dbl(s(z0))) → c4(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 326.74/101.22
ACTIVE(add(s(z0), z1)) → c6(S(add(z0, z1)), ADD(z0, z1)) 326.74/101.22
ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2)) 326.74/101.22
ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.22
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.22
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.22
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.22
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.22
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.22
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.22
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.22
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.22
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.22
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.22
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.22
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.22
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.22
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.22
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.22
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.22
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.22
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.22
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.22
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.22
S(ok(z0)) → c44(S(z0)) 326.74/101.22
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 326.74/101.22
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0))

K tuples:none
Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c, c2, c4, c6, c8, 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, c40, c41, c42, c44, c45, c46

326.74/101.22

(3) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing tuple parts

326.74/101.22

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 326.74/101.22
active(sqr(0)) → mark(0) 326.74/101.22
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 326.74/101.22
active(dbl(0)) → mark(0) 326.74/101.22
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 326.74/101.22
active(add(0, z0)) → mark(z0) 326.74/101.22
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 326.74/101.22
active(first(0, z0)) → mark(nil) 326.74/101.22
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 326.74/101.22
active(terms(z0)) → terms(active(z0)) 326.74/101.22
active(cons(z0, z1)) → cons(active(z0), z1) 326.74/101.22
active(recip(z0)) → recip(active(z0)) 326.74/101.22
active(sqr(z0)) → sqr(active(z0)) 326.74/101.22
active(add(z0, z1)) → add(active(z0), z1) 326.74/101.22
active(add(z0, z1)) → add(z0, active(z1)) 326.74/101.22
active(dbl(z0)) → dbl(active(z0)) 326.74/101.22
active(first(z0, z1)) → first(active(z0), z1) 326.74/101.22
active(first(z0, z1)) → first(z0, active(z1)) 326.74/101.22
terms(mark(z0)) → mark(terms(z0)) 326.74/101.22
terms(ok(z0)) → ok(terms(z0)) 326.74/101.22
cons(mark(z0), z1) → mark(cons(z0, z1)) 326.74/101.22
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 326.74/101.22
recip(mark(z0)) → mark(recip(z0)) 326.74/101.22
recip(ok(z0)) → ok(recip(z0)) 326.74/101.22
sqr(mark(z0)) → mark(sqr(z0)) 326.74/101.22
sqr(ok(z0)) → ok(sqr(z0)) 326.74/101.22
add(mark(z0), z1) → mark(add(z0, z1)) 326.74/101.22
add(z0, mark(z1)) → mark(add(z0, z1)) 326.74/101.22
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 326.74/101.22
dbl(mark(z0)) → mark(dbl(z0)) 326.74/101.22
dbl(ok(z0)) → ok(dbl(z0)) 326.74/101.22
first(mark(z0), z1) → mark(first(z0, z1)) 326.74/101.22
first(z0, mark(z1)) → mark(first(z0, z1)) 326.74/101.22
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 326.74/101.22
proper(terms(z0)) → terms(proper(z0)) 326.74/101.22
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 326.74/101.22
proper(recip(z0)) → recip(proper(z0)) 326.74/101.22
proper(sqr(z0)) → sqr(proper(z0)) 326.74/101.22
proper(s(z0)) → s(proper(z0)) 326.74/101.22
proper(0) → ok(0) 326.74/101.22
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 326.74/101.22
proper(dbl(z0)) → dbl(proper(z0)) 326.74/101.22
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 326.74/101.22
proper(nil) → ok(nil) 326.74/101.22
s(ok(z0)) → ok(s(z0)) 326.74/101.22
top(mark(z0)) → top(proper(z0)) 326.74/101.22
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sqr(s(z0))) → c2(S(add(sqr(z0), dbl(z0))), ADD(sqr(z0), dbl(z0)), SQR(z0), DBL(z0)) 326.74/101.22
ACTIVE(dbl(s(z0))) → c4(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 326.74/101.22
ACTIVE(add(s(z0), z1)) → c6(S(add(z0, z1)), ADD(z0, z1)) 326.74/101.22
ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2)) 326.74/101.22
ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.22
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.22
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.22
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.22
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.22
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.22
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.22
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.22
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.22
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.22
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.22
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.22
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.22
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.22
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.22
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.22
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.22
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.22
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.22
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.22
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.22
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.22
S(ok(z0)) → c44(S(z0)) 326.74/101.22
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 326.74/101.22
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(terms(z0)) → c(SQR(z0), S(z0))

S tuples:

ACTIVE(sqr(s(z0))) → c2(S(add(sqr(z0), dbl(z0))), ADD(sqr(z0), dbl(z0)), SQR(z0), DBL(z0)) 326.74/101.22
ACTIVE(dbl(s(z0))) → c4(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 326.74/101.22
ACTIVE(add(s(z0), z1)) → c6(S(add(z0, z1)), ADD(z0, z1)) 326.74/101.22
ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2)) 326.74/101.22
ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.22
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.22
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.22
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.22
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.22
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.22
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.22
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.22
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.23
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.23
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.23
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.23
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.23
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.23
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.23
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.23
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.23
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.23
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.23
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.23
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.23
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.23
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.23
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.23
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.23
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.23
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.23
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.23
S(ok(z0)) → c44(S(z0)) 326.74/101.23
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 326.74/101.23
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.23
ACTIVE(terms(z0)) → c(SQR(z0), S(z0))

K tuples:none
Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c2, c4, c6, c8, 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, c40, c41, c42, c44, c45, c46, c

326.74/101.23

(5) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC

326.74/101.23

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 326.74/101.23
active(sqr(0)) → mark(0) 326.74/101.23
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 326.74/101.23
active(dbl(0)) → mark(0) 326.74/101.23
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 326.74/101.23
active(add(0, z0)) → mark(z0) 326.74/101.23
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 326.74/101.23
active(first(0, z0)) → mark(nil) 326.74/101.23
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 326.74/101.23
active(terms(z0)) → terms(active(z0)) 326.74/101.23
active(cons(z0, z1)) → cons(active(z0), z1) 326.74/101.23
active(recip(z0)) → recip(active(z0)) 326.74/101.23
active(sqr(z0)) → sqr(active(z0)) 326.74/101.23
active(add(z0, z1)) → add(active(z0), z1) 326.74/101.23
active(add(z0, z1)) → add(z0, active(z1)) 326.74/101.23
active(dbl(z0)) → dbl(active(z0)) 326.74/101.23
active(first(z0, z1)) → first(active(z0), z1) 326.74/101.23
active(first(z0, z1)) → first(z0, active(z1)) 326.74/101.23
terms(mark(z0)) → mark(terms(z0)) 326.74/101.23
terms(ok(z0)) → ok(terms(z0)) 326.74/101.23
cons(mark(z0), z1) → mark(cons(z0, z1)) 326.74/101.23
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 326.74/101.23
recip(mark(z0)) → mark(recip(z0)) 326.74/101.23
recip(ok(z0)) → ok(recip(z0)) 326.74/101.23
sqr(mark(z0)) → mark(sqr(z0)) 326.74/101.23
sqr(ok(z0)) → ok(sqr(z0)) 326.74/101.23
add(mark(z0), z1) → mark(add(z0, z1)) 326.74/101.23
add(z0, mark(z1)) → mark(add(z0, z1)) 326.74/101.23
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 326.74/101.23
dbl(mark(z0)) → mark(dbl(z0)) 326.74/101.23
dbl(ok(z0)) → ok(dbl(z0)) 326.74/101.23
first(mark(z0), z1) → mark(first(z0, z1)) 326.74/101.23
first(z0, mark(z1)) → mark(first(z0, z1)) 326.74/101.23
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 326.74/101.23
proper(terms(z0)) → terms(proper(z0)) 326.74/101.23
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 326.74/101.23
proper(recip(z0)) → recip(proper(z0)) 326.74/101.23
proper(sqr(z0)) → sqr(proper(z0)) 326.74/101.23
proper(s(z0)) → s(proper(z0)) 326.74/101.23
proper(0) → ok(0) 326.74/101.23
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 326.74/101.23
proper(dbl(z0)) → dbl(proper(z0)) 326.74/101.23
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 326.74/101.23
proper(nil) → ok(nil) 326.74/101.23
s(ok(z0)) → ok(s(z0)) 326.74/101.23
top(mark(z0)) → top(proper(z0)) 326.74/101.23
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 326.74/101.23
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 326.74/101.23
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.23
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.23
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.23
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.23
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.23
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.23
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.23
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.23
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.23
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.23
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.23
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.23
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.23
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.23
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.23
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.23
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.23
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.23
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.23
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.23
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.23
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.23
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.23
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.23
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.23
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.23
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.23
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.23
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.23
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.23
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.23
S(ok(z0)) → c44(S(z0)) 326.74/101.23
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 326.74/101.23
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.23
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 326.74/101.23
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 326.74/101.23
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 326.74/101.23
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 326.74/101.23
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 326.74/101.23
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 326.74/101.23
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 326.74/101.23
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 326.74/101.23
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 326.74/101.23
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 326.74/101.23
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 326.74/101.23
ACTIVE(terms(z0)) → c1(SQR(z0)) 326.74/101.23
ACTIVE(terms(z0)) → c1(S(z0))

S tuples:

ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 326.74/101.23
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 326.74/101.23
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.23
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.23
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.23
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.23
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.23
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.23
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.23
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.23
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.23
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.30
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.30
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.30
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.30
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.30
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.30
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.30
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.30
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.30
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.30
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.30
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.30
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.30
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.30
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
S(ok(z0)) → c44(S(z0)) 326.74/101.30
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 326.74/101.30
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 326.74/101.30
ACTIVE(terms(z0)) → c1(SQR(z0)) 326.74/101.30
ACTIVE(terms(z0)) → c1(S(z0))

K tuples:none
Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

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, c40, c41, c42, c44, c45, c46, c1

326.74/101.30

(7) 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.

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

We considered the (Usable) Rules:

first(mark(z0), z1) → mark(first(z0, z1)) 326.74/101.30
first(z0, mark(z1)) → mark(first(z0, z1)) 326.74/101.30
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 326.74/101.30
add(mark(z0), z1) → mark(add(z0, z1)) 326.74/101.30
add(z0, mark(z1)) → mark(add(z0, z1)) 326.74/101.30
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 326.74/101.30
dbl(mark(z0)) → mark(dbl(z0)) 326.74/101.30
dbl(ok(z0)) → ok(dbl(z0)) 326.74/101.30
s(ok(z0)) → ok(s(z0)) 326.74/101.30
sqr(mark(z0)) → mark(sqr(z0)) 326.74/101.30
sqr(ok(z0)) → ok(sqr(z0)) 326.74/101.30
active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 326.74/101.30
active(sqr(0)) → mark(0) 326.74/101.30
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 326.74/101.30
active(dbl(0)) → mark(0) 326.74/101.30
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 326.74/101.30
active(add(0, z0)) → mark(z0) 326.74/101.30
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 326.74/101.30
active(first(0, z0)) → mark(nil) 326.74/101.30
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 326.74/101.30
active(terms(z0)) → terms(active(z0)) 326.74/101.30
active(cons(z0, z1)) → cons(active(z0), z1) 326.74/101.30
active(recip(z0)) → recip(active(z0)) 326.74/101.30
active(sqr(z0)) → sqr(active(z0)) 326.74/101.30
active(add(z0, z1)) → add(active(z0), z1) 326.74/101.30
active(add(z0, z1)) → add(z0, active(z1)) 326.74/101.30
active(dbl(z0)) → dbl(active(z0)) 326.74/101.30
active(first(z0, z1)) → first(active(z0), z1) 326.74/101.30
active(first(z0, z1)) → first(z0, active(z1)) 326.74/101.30
recip(mark(z0)) → mark(recip(z0)) 326.74/101.30
recip(ok(z0)) → ok(recip(z0)) 326.74/101.30
cons(mark(z0), z1) → mark(cons(z0, z1)) 326.74/101.30
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 326.74/101.30
terms(mark(z0)) → mark(terms(z0)) 326.74/101.30
terms(ok(z0)) → ok(terms(z0)) 326.74/101.30
proper(terms(z0)) → terms(proper(z0)) 326.74/101.30
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 326.74/101.30
proper(recip(z0)) → recip(proper(z0)) 326.74/101.30
proper(sqr(z0)) → sqr(proper(z0)) 326.74/101.30
proper(s(z0)) → s(proper(z0)) 326.74/101.30
proper(0) → ok(0) 326.74/101.30
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 326.74/101.30
proper(dbl(z0)) → dbl(proper(z0)) 326.74/101.30
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 326.74/101.30
proper(nil) → ok(nil)

And the Tuples:

ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.30
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.30
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.30
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.30
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.30
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.30
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.30
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.30
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.30
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.30
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.30
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.30
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.30
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.30
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.30
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.30
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
S(ok(z0)) → c44(S(z0)) 326.74/101.30
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 326.74/101.30
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 326.74/101.30
ACTIVE(terms(z0)) → c1(SQR(z0)) 326.74/101.30
ACTIVE(terms(z0)) → c1(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 326.74/101.30

POL(0) = [2] 326.74/101.30
POL(ACTIVE(x₁)) = 0 326.74/101.30
POL(ADD(x₁, x₂)) = 0 326.74/101.30
POL(CONS(x₁, x₂)) = 0 326.74/101.30
POL(DBL(x₁)) = 0 326.74/101.30
POL(FIRST(x₁, x₂)) = 0 326.74/101.30
POL(PROPER(x₁)) = 0 326.74/101.30
POL(RECIP(x₁)) = 0 326.74/101.30
POL(S(x₁)) = 0 326.74/101.30
POL(SQR(x₁)) = 0 326.74/101.30
POL(TERMS(x₁)) = 0 326.74/101.30
POL(TOP(x₁)) = x₁ 326.74/101.30
POL(active(x₁)) = x₁ 326.74/101.30
POL(add(x₁, x₂)) = [2]x₁ + x₂ 326.74/101.30
POL(c1(x₁)) = x₁ 326.74/101.30
POL(c10(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c11(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c12(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c13(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c14(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c15(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c16(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c17(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c18(x₁)) = x₁ 326.74/101.30
POL(c19(x₁)) = x₁ 326.74/101.30
POL(c20(x₁)) = x₁ 326.74/101.30
POL(c21(x₁)) = x₁ 326.74/101.30
POL(c22(x₁)) = x₁ 326.74/101.30
POL(c23(x₁)) = x₁ 326.74/101.30
POL(c24(x₁)) = x₁ 326.74/101.30
POL(c25(x₁)) = x₁ 326.74/101.30
POL(c26(x₁)) = x₁ 326.74/101.30
POL(c27(x₁)) = x₁ 326.74/101.30
POL(c28(x₁)) = x₁ 326.74/101.30
POL(c29(x₁)) = x₁ 326.74/101.30
POL(c30(x₁)) = x₁ 326.74/101.30
POL(c31(x₁)) = x₁ 326.74/101.30
POL(c32(x₁)) = x₁ 326.74/101.30
POL(c33(x₁)) = x₁ 326.74/101.30
POL(c34(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c35(x₁, x₂, x₃)) = x₁ + x₂ + x₃ 326.74/101.30
POL(c36(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c37(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c38(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c40(x₁, x₂, x₃)) = x₁ + x₂ + x₃ 326.74/101.30
POL(c41(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c42(x₁, x₂, x₃)) = x₁ + x₂ + x₃ 326.74/101.30
POL(c44(x₁)) = x₁ 326.74/101.30
POL(c45(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c46(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(c9(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(cons(x₁, x₂)) = [2]x₁ 326.74/101.30
POL(dbl(x₁)) = [4]x₁ 326.74/101.30
POL(first(x₁, x₂)) = x₁ + x₂ 326.74/101.30
POL(mark(x₁)) = [1] + x₁ 326.74/101.30
POL(nil) = 0 326.74/101.30
POL(ok(x₁)) = x₁ 326.74/101.30
POL(proper(x₁)) = x₁ 326.74/101.30
POL(recip(x₁)) = x₁ 326.74/101.30
POL(s(x₁)) = [1] 326.74/101.30
POL(sqr(x₁)) = [2]x₁ 326.74/101.30
POL(terms(x₁)) = [1] + [4]x₁

326.74/101.30

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 326.74/101.30
active(sqr(0)) → mark(0) 326.74/101.30
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 326.74/101.30
active(dbl(0)) → mark(0) 326.74/101.30
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 326.74/101.30
active(add(0, z0)) → mark(z0) 326.74/101.30
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 326.74/101.30
active(first(0, z0)) → mark(nil) 326.74/101.30
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 326.74/101.30
active(terms(z0)) → terms(active(z0)) 326.74/101.30
active(cons(z0, z1)) → cons(active(z0), z1) 326.74/101.30
active(recip(z0)) → recip(active(z0)) 326.74/101.30
active(sqr(z0)) → sqr(active(z0)) 326.74/101.30
active(add(z0, z1)) → add(active(z0), z1) 326.74/101.30
active(add(z0, z1)) → add(z0, active(z1)) 326.74/101.30
active(dbl(z0)) → dbl(active(z0)) 326.74/101.30
active(first(z0, z1)) → first(active(z0), z1) 326.74/101.30
active(first(z0, z1)) → first(z0, active(z1)) 326.74/101.30
terms(mark(z0)) → mark(terms(z0)) 326.74/101.30
terms(ok(z0)) → ok(terms(z0)) 326.74/101.30
cons(mark(z0), z1) → mark(cons(z0, z1)) 326.74/101.30
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 326.74/101.30
recip(mark(z0)) → mark(recip(z0)) 326.74/101.30
recip(ok(z0)) → ok(recip(z0)) 326.74/101.30
sqr(mark(z0)) → mark(sqr(z0)) 326.74/101.30
sqr(ok(z0)) → ok(sqr(z0)) 326.74/101.30
add(mark(z0), z1) → mark(add(z0, z1)) 326.74/101.30
add(z0, mark(z1)) → mark(add(z0, z1)) 326.74/101.30
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 326.74/101.30
dbl(mark(z0)) → mark(dbl(z0)) 326.74/101.30
dbl(ok(z0)) → ok(dbl(z0)) 326.74/101.30
first(mark(z0), z1) → mark(first(z0, z1)) 326.74/101.30
first(z0, mark(z1)) → mark(first(z0, z1)) 326.74/101.30
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 326.74/101.30
proper(terms(z0)) → terms(proper(z0)) 326.74/101.30
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 326.74/101.30
proper(recip(z0)) → recip(proper(z0)) 326.74/101.30
proper(sqr(z0)) → sqr(proper(z0)) 326.74/101.30
proper(s(z0)) → s(proper(z0)) 326.74/101.30
proper(0) → ok(0) 326.74/101.30
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 326.74/101.30
proper(dbl(z0)) → dbl(proper(z0)) 326.74/101.30
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 326.74/101.30
proper(nil) → ok(nil) 326.74/101.30
s(ok(z0)) → ok(s(z0)) 326.74/101.30
top(mark(z0)) → top(proper(z0)) 326.74/101.30
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.30
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.30
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.30
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.30
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.30
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.30
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.30
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.30
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.30
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.30
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.30
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.30
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.30
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.30
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.30
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.30
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
S(ok(z0)) → c44(S(z0)) 326.74/101.30
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 326.74/101.30
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 326.74/101.30
ACTIVE(terms(z0)) → c1(SQR(z0)) 326.74/101.30
ACTIVE(terms(z0)) → c1(S(z0))

S tuples:

ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.30
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.30
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.30
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.30
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.30
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.30
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.30
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.30
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.30
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.30
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.30
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.30
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.30
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.30
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.30
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.30
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
S(ok(z0)) → c44(S(z0)) 326.74/101.30
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 326.74/101.30
ACTIVE(terms(z0)) → c1(SQR(z0)) 326.74/101.30
ACTIVE(terms(z0)) → c1(S(z0))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

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, c40, c41, c42, c44, c45, c46, c1

326.74/101.30

(9) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) by

ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 326.74/101.30
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 326.74/101.30
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 326.74/101.30
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 326.74/101.30
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 326.74/101.30
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 326.74/101.30
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 326.74/101.30
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.30
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 326.74/101.30
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 326.74/101.30
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 326.74/101.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 326.74/101.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 326.74/101.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))

326.74/101.30

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 326.74/101.30
active(sqr(0)) → mark(0) 326.74/101.30
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 326.74/101.30
active(dbl(0)) → mark(0) 326.74/101.30
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 326.74/101.30
active(add(0, z0)) → mark(z0) 326.74/101.30
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 326.74/101.30
active(first(0, z0)) → mark(nil) 326.74/101.30
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 326.74/101.30
active(terms(z0)) → terms(active(z0)) 326.74/101.30
active(cons(z0, z1)) → cons(active(z0), z1) 326.74/101.30
active(recip(z0)) → recip(active(z0)) 326.74/101.30
active(sqr(z0)) → sqr(active(z0)) 326.74/101.30
active(add(z0, z1)) → add(active(z0), z1) 326.74/101.30
active(add(z0, z1)) → add(z0, active(z1)) 326.74/101.30
active(dbl(z0)) → dbl(active(z0)) 326.74/101.30
active(first(z0, z1)) → first(active(z0), z1) 326.74/101.30
active(first(z0, z1)) → first(z0, active(z1)) 326.74/101.30
terms(mark(z0)) → mark(terms(z0)) 326.74/101.30
terms(ok(z0)) → ok(terms(z0)) 326.74/101.30
cons(mark(z0), z1) → mark(cons(z0, z1)) 326.74/101.30
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 326.74/101.30
recip(mark(z0)) → mark(recip(z0)) 326.74/101.30
recip(ok(z0)) → ok(recip(z0)) 326.74/101.30
sqr(mark(z0)) → mark(sqr(z0)) 326.74/101.30
sqr(ok(z0)) → ok(sqr(z0)) 326.74/101.30
add(mark(z0), z1) → mark(add(z0, z1)) 326.74/101.30
add(z0, mark(z1)) → mark(add(z0, z1)) 326.74/101.30
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 326.74/101.30
dbl(mark(z0)) → mark(dbl(z0)) 326.74/101.30
dbl(ok(z0)) → ok(dbl(z0)) 326.74/101.30
first(mark(z0), z1) → mark(first(z0, z1)) 326.74/101.30
first(z0, mark(z1)) → mark(first(z0, z1)) 326.74/101.30
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 326.74/101.30
proper(terms(z0)) → terms(proper(z0)) 326.74/101.30
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 326.74/101.30
proper(recip(z0)) → recip(proper(z0)) 326.74/101.30
proper(sqr(z0)) → sqr(proper(z0)) 326.74/101.30
proper(s(z0)) → s(proper(z0)) 326.74/101.30
proper(0) → ok(0) 326.74/101.30
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 326.74/101.30
proper(dbl(z0)) → dbl(proper(z0)) 326.74/101.30
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 326.74/101.30
proper(nil) → ok(nil) 326.74/101.30
s(ok(z0)) → ok(s(z0)) 326.74/101.30
top(mark(z0)) → top(proper(z0)) 326.74/101.30
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.30
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.30
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.30
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.30
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.30
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.30
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.30
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.30
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.30
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.30
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.30
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.30
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.30
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.30
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.30
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.30
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
S(ok(z0)) → c44(S(z0)) 326.74/101.30
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 326.74/101.30
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 326.74/101.30
ACTIVE(terms(z0)) → c1(SQR(z0)) 326.74/101.30
ACTIVE(terms(z0)) → c1(S(z0)) 326.74/101.30
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 326.74/101.30
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 326.74/101.30
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 326.74/101.30
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 326.74/101.30
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 326.74/101.30
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 326.74/101.30
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 326.74/101.30
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.30
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 326.74/101.30
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 326.74/101.30
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 326.74/101.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 326.74/101.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 326.74/101.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))

S tuples:

ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.30
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.30
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.30
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.30
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.30
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.30
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.30
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.30
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.30
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.30
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.30
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.30
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.30
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.30
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.30
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.30
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
S(ok(z0)) → c44(S(z0)) 326.74/101.30
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 326.74/101.30
ACTIVE(terms(z0)) → c1(SQR(z0)) 326.74/101.30
ACTIVE(terms(z0)) → c1(S(z0)) 326.74/101.30
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 326.74/101.30
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 326.74/101.30
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 326.74/101.30
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 326.74/101.30
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 326.74/101.30
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 326.74/101.30
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 326.74/101.30
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.30
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 326.74/101.30
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 326.74/101.30
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 326.74/101.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 326.74/101.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 326.74/101.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c40, c41, c42, c44, c45, c46, c1, c9

326.74/101.30

(11) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) by

ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 326.74/101.30
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 326.74/101.30
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 326.74/101.30
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 326.74/101.30
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 326.74/101.30
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 326.74/101.30
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 326.74/101.30
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.30
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 326.74/101.30
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 326.74/101.30
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 326.74/101.30
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 326.74/101.30
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 326.74/101.30
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))

326.74/101.30

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 326.74/101.30
active(sqr(0)) → mark(0) 326.74/101.30
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 326.74/101.30
active(dbl(0)) → mark(0) 326.74/101.30
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 326.74/101.30
active(add(0, z0)) → mark(z0) 326.74/101.30
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 326.74/101.30
active(first(0, z0)) → mark(nil) 326.74/101.30
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 326.74/101.30
active(terms(z0)) → terms(active(z0)) 326.74/101.30
active(cons(z0, z1)) → cons(active(z0), z1) 326.74/101.30
active(recip(z0)) → recip(active(z0)) 326.74/101.30
active(sqr(z0)) → sqr(active(z0)) 326.74/101.30
active(add(z0, z1)) → add(active(z0), z1) 326.74/101.30
active(add(z0, z1)) → add(z0, active(z1)) 326.74/101.30
active(dbl(z0)) → dbl(active(z0)) 326.74/101.30
active(first(z0, z1)) → first(active(z0), z1) 326.74/101.30
active(first(z0, z1)) → first(z0, active(z1)) 326.74/101.30
terms(mark(z0)) → mark(terms(z0)) 326.74/101.30
terms(ok(z0)) → ok(terms(z0)) 326.74/101.30
cons(mark(z0), z1) → mark(cons(z0, z1)) 326.74/101.30
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 326.74/101.30
recip(mark(z0)) → mark(recip(z0)) 326.74/101.30
recip(ok(z0)) → ok(recip(z0)) 326.74/101.30
sqr(mark(z0)) → mark(sqr(z0)) 326.74/101.30
sqr(ok(z0)) → ok(sqr(z0)) 326.74/101.30
add(mark(z0), z1) → mark(add(z0, z1)) 326.74/101.30
add(z0, mark(z1)) → mark(add(z0, z1)) 326.74/101.30
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 326.74/101.30
dbl(mark(z0)) → mark(dbl(z0)) 326.74/101.30
dbl(ok(z0)) → ok(dbl(z0)) 326.74/101.30
first(mark(z0), z1) → mark(first(z0, z1)) 326.74/101.30
first(z0, mark(z1)) → mark(first(z0, z1)) 326.74/101.30
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 326.74/101.30
proper(terms(z0)) → terms(proper(z0)) 326.74/101.30
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 326.74/101.30
proper(recip(z0)) → recip(proper(z0)) 326.74/101.30
proper(sqr(z0)) → sqr(proper(z0)) 326.74/101.30
proper(s(z0)) → s(proper(z0)) 326.74/101.30
proper(0) → ok(0) 326.74/101.30
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 326.74/101.30
proper(dbl(z0)) → dbl(proper(z0)) 326.74/101.30
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 326.74/101.30
proper(nil) → ok(nil) 326.74/101.30
s(ok(z0)) → ok(s(z0)) 326.74/101.30
top(mark(z0)) → top(proper(z0)) 326.74/101.30
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.30
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.30
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.30
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.30
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.30
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.30
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.30
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.30
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.30
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.30
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.30
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.30
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.30
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.30
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.30
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.30
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
S(ok(z0)) → c44(S(z0)) 326.74/101.30
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 326.74/101.30
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 326.74/101.30
ACTIVE(terms(z0)) → c1(SQR(z0)) 326.74/101.30
ACTIVE(terms(z0)) → c1(S(z0)) 326.74/101.30
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 326.74/101.30
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 326.74/101.30
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 326.74/101.30
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 326.74/101.30
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 326.74/101.30
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 326.74/101.30
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 326.74/101.30
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.30
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 326.74/101.30
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 326.74/101.30
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 326.74/101.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 326.74/101.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 326.74/101.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 326.74/101.30
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 326.74/101.30
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 326.74/101.30
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 326.74/101.30
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 326.74/101.30
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 326.74/101.30
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 326.74/101.30
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 326.74/101.30
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.30
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 326.74/101.30
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 326.74/101.30
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 326.74/101.30
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 326.74/101.30
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 326.74/101.30
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))

S tuples:

ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.30
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.30
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.30
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.30
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.30
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.30
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.30
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.30
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.30
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.30
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.30
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.30
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.30
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.30
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.30
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.30
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.30
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.30
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.30
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.30
S(ok(z0)) → c44(S(z0)) 326.74/101.30
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 326.74/101.30
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 326.74/101.30
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 326.74/101.30
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 326.74/101.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 326.74/101.30
ACTIVE(terms(z0)) → c1(SQR(z0)) 326.74/101.30
ACTIVE(terms(z0)) → c1(S(z0)) 326.74/101.30
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 326.74/101.30
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 326.74/101.30
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 326.74/101.30
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 326.74/101.30
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 326.74/101.30
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 326.74/101.30
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 326.74/101.30
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.30
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 326.74/101.30
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 326.74/101.30
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 326.74/101.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 326.74/101.30
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 326.74/101.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 326.74/101.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 326.74/101.30
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 326.74/101.30
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 326.74/101.30
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 326.74/101.30
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 326.74/101.30
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 326.74/101.30
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 326.74/101.30
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 326.74/101.30
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 326.74/101.31
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 326.74/101.31
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 326.74/101.31
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 326.74/101.31
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 326.74/101.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 326.74/101.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 326.74/101.31
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 326.74/101.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 326.74/101.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

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, c40, c41, c42, c44, c45, c46, c1, c9, c10

326.74/101.31

(13) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) by

ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 326.74/101.31
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0)), ACTIVE(sqr(0))) 326.74/101.31
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 326.74/101.31
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 326.74/101.31
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 326.74/101.31
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 326.74/101.31
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 326.74/101.31
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 326.74/101.31
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.31
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 326.74/101.31
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 326.74/101.31
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 326.74/101.31
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 326.74/101.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 326.74/101.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 326.74/101.31
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 326.74/101.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 326.74/101.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

326.74/101.31

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 326.74/101.31
active(sqr(0)) → mark(0) 326.74/101.31
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 326.74/101.31
active(dbl(0)) → mark(0) 326.74/101.31
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 326.74/101.31
active(add(0, z0)) → mark(z0) 326.74/101.31
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 326.74/101.31
active(first(0, z0)) → mark(nil) 326.74/101.31
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 326.74/101.31
active(terms(z0)) → terms(active(z0)) 326.74/101.31
active(cons(z0, z1)) → cons(active(z0), z1) 326.74/101.31
active(recip(z0)) → recip(active(z0)) 326.74/101.31
active(sqr(z0)) → sqr(active(z0)) 326.74/101.31
active(add(z0, z1)) → add(active(z0), z1) 326.74/101.31
active(add(z0, z1)) → add(z0, active(z1)) 326.74/101.31
active(dbl(z0)) → dbl(active(z0)) 326.74/101.31
active(first(z0, z1)) → first(active(z0), z1) 326.74/101.31
active(first(z0, z1)) → first(z0, active(z1)) 326.74/101.31
terms(mark(z0)) → mark(terms(z0)) 326.74/101.31
terms(ok(z0)) → ok(terms(z0)) 326.74/101.31
cons(mark(z0), z1) → mark(cons(z0, z1)) 326.74/101.31
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 326.74/101.31
recip(mark(z0)) → mark(recip(z0)) 326.74/101.31
recip(ok(z0)) → ok(recip(z0)) 326.74/101.31
sqr(mark(z0)) → mark(sqr(z0)) 326.74/101.31
sqr(ok(z0)) → ok(sqr(z0)) 326.74/101.31
add(mark(z0), z1) → mark(add(z0, z1)) 326.74/101.31
add(z0, mark(z1)) → mark(add(z0, z1)) 326.74/101.31
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 326.74/101.31
dbl(mark(z0)) → mark(dbl(z0)) 326.74/101.31
dbl(ok(z0)) → ok(dbl(z0)) 326.74/101.31
first(mark(z0), z1) → mark(first(z0, z1)) 326.74/101.31
first(z0, mark(z1)) → mark(first(z0, z1)) 326.74/101.31
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 326.74/101.31
proper(terms(z0)) → terms(proper(z0)) 326.74/101.31
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 326.74/101.31
proper(recip(z0)) → recip(proper(z0)) 326.74/101.31
proper(sqr(z0)) → sqr(proper(z0)) 326.74/101.31
proper(s(z0)) → s(proper(z0)) 326.74/101.31
proper(0) → ok(0) 326.74/101.31
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 326.74/101.31
proper(dbl(z0)) → dbl(proper(z0)) 326.74/101.31
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 326.74/101.31
proper(nil) → ok(nil) 326.74/101.31
s(ok(z0)) → ok(s(z0)) 326.74/101.31
top(mark(z0)) → top(proper(z0)) 326.74/101.31
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.31
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.31
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.31
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.31
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.31
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.31
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.31
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.31
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.31
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.31
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.31
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.31
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.31
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.31
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.31
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.31
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.31
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.31
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.31
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.31
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.31
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.31
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.31
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.31
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.31
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.31
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.31
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.31
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.31
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.31
S(ok(z0)) → c44(S(z0)) 326.74/101.31
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 326.74/101.31
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.31
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 326.74/101.31
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 326.74/101.31
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 326.74/101.31
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 326.74/101.31
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 326.74/101.31
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 326.74/101.31
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 326.74/101.31
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 326.74/101.31
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 326.74/101.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 326.74/101.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 326.74/101.31
ACTIVE(terms(z0)) → c1(SQR(z0)) 326.74/101.31
ACTIVE(terms(z0)) → c1(S(z0)) 326.74/101.31
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 326.74/101.31
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 326.74/101.31
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 326.74/101.31
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 326.74/101.31
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 326.74/101.31
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 326.74/101.31
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 326.74/101.31
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 326.74/101.31
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.31
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 326.74/101.31
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 326.74/101.31
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 326.74/101.31
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 326.74/101.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 326.74/101.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 326.74/101.31
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 326.74/101.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 326.74/101.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 326.74/101.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 326.74/101.31
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 326.74/101.31
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 326.74/101.31
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 326.74/101.31
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 326.74/101.31
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 326.74/101.31
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 326.74/101.31
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 326.74/101.31
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 326.74/101.31
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 326.74/101.31
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 326.74/101.31
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 326.74/101.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 326.74/101.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 326.74/101.31
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 326.74/101.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 326.74/101.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 326.74/101.31
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 326.74/101.31
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0)), ACTIVE(sqr(0))) 326.74/101.31
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 326.74/101.31
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 326.74/101.31
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 326.74/101.31
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 326.74/101.31
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 326.74/101.31
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 326.74/101.31
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 326.74/101.31
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 326.74/101.31
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 326.74/101.31
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 326.74/101.31
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 326.74/101.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 326.74/101.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 326.74/101.31
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 326.74/101.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 326.74/101.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

S tuples:

ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 326.74/101.31
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 326.74/101.31
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 326.74/101.31
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 326.74/101.31
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 326.74/101.31
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 326.74/101.31
TERMS(mark(z0)) → c18(TERMS(z0)) 326.74/101.31
TERMS(ok(z0)) → c19(TERMS(z0)) 326.74/101.31
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 326.74/101.31
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 326.74/101.31
RECIP(mark(z0)) → c22(RECIP(z0)) 326.74/101.31
RECIP(ok(z0)) → c23(RECIP(z0)) 326.74/101.31
SQR(mark(z0)) → c24(SQR(z0)) 326.74/101.31
SQR(ok(z0)) → c25(SQR(z0)) 326.74/101.31
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 326.74/101.31
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 326.74/101.31
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 326.74/101.31
DBL(mark(z0)) → c29(DBL(z0)) 326.74/101.31
DBL(ok(z0)) → c30(DBL(z0)) 326.74/101.31
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 326.74/101.31
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 326.74/101.31
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 326.74/101.31
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 326.74/101.31
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.31
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 326.74/101.31
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 326.74/101.31
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 326.74/101.31
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.31
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 326.74/101.31
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 326.74/101.31
S(ok(z0)) → c44(S(z0)) 326.74/101.31
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 326.74/101.31
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 326.74/101.31
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 326.74/101.31
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 326.74/101.31
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 326.74/101.31
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 326.74/101.31
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 326.74/101.31
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 326.74/101.31
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 326.74/101.31
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 326.74/101.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 326.74/101.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 326.74/101.31
ACTIVE(terms(z0)) → c1(SQR(z0)) 326.74/101.31
ACTIVE(terms(z0)) → c1(S(z0)) 326.74/101.31
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 326.74/101.31
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 326.74/101.31
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 326.74/101.31
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 326.74/101.31
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 326.74/101.31
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 326.74/101.31
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 326.74/101.31
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.31
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.31
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.31
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.31
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 327.12/101.31
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 327.12/101.31
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 327.12/101.31
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 327.12/101.31
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.12/101.31
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.12/101.31
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.12/101.31
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.12/101.31
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.12/101.31
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.12/101.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.12/101.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0)), ACTIVE(sqr(0))) 327.12/101.31
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.31
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 327.12/101.31
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.31
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.31
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.31
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.31
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.31
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.31
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.31
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

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, c40, c41, c42, c44, c45, c46, c1, c9, c10, c11

327.12/101.31

(15) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) by

ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0)), ACTIVE(sqr(0))) 327.12/101.31
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.31
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 327.12/101.31
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.31
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.31
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.31
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.31
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.31
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.31
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.31
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.31
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.31
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))

327.12/101.31

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.12/101.31
active(sqr(0)) → mark(0) 327.12/101.31
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.12/101.31
active(dbl(0)) → mark(0) 327.12/101.31
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.12/101.31
active(add(0, z0)) → mark(z0) 327.12/101.31
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.12/101.31
active(first(0, z0)) → mark(nil) 327.12/101.31
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.12/101.31
active(terms(z0)) → terms(active(z0)) 327.12/101.31
active(cons(z0, z1)) → cons(active(z0), z1) 327.12/101.31
active(recip(z0)) → recip(active(z0)) 327.12/101.31
active(sqr(z0)) → sqr(active(z0)) 327.12/101.31
active(add(z0, z1)) → add(active(z0), z1) 327.12/101.31
active(add(z0, z1)) → add(z0, active(z1)) 327.12/101.31
active(dbl(z0)) → dbl(active(z0)) 327.12/101.31
active(first(z0, z1)) → first(active(z0), z1) 327.12/101.31
active(first(z0, z1)) → first(z0, active(z1)) 327.12/101.31
terms(mark(z0)) → mark(terms(z0)) 327.12/101.31
terms(ok(z0)) → ok(terms(z0)) 327.12/101.31
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.12/101.31
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.12/101.31
recip(mark(z0)) → mark(recip(z0)) 327.12/101.31
recip(ok(z0)) → ok(recip(z0)) 327.12/101.31
sqr(mark(z0)) → mark(sqr(z0)) 327.12/101.31
sqr(ok(z0)) → ok(sqr(z0)) 327.12/101.31
add(mark(z0), z1) → mark(add(z0, z1)) 327.12/101.31
add(z0, mark(z1)) → mark(add(z0, z1)) 327.12/101.31
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.12/101.31
dbl(mark(z0)) → mark(dbl(z0)) 327.12/101.31
dbl(ok(z0)) → ok(dbl(z0)) 327.12/101.31
first(mark(z0), z1) → mark(first(z0, z1)) 327.12/101.31
first(z0, mark(z1)) → mark(first(z0, z1)) 327.12/101.31
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.12/101.31
proper(terms(z0)) → terms(proper(z0)) 327.12/101.31
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.12/101.31
proper(recip(z0)) → recip(proper(z0)) 327.12/101.31
proper(sqr(z0)) → sqr(proper(z0)) 327.12/101.31
proper(s(z0)) → s(proper(z0)) 327.12/101.31
proper(0) → ok(0) 327.12/101.31
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.12/101.31
proper(dbl(z0)) → dbl(proper(z0)) 327.12/101.31
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.12/101.31
proper(nil) → ok(nil) 327.12/101.31
s(ok(z0)) → ok(s(z0)) 327.12/101.31
top(mark(z0)) → top(proper(z0)) 327.12/101.31
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.12/101.31
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.12/101.31
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 327.12/101.31
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.12/101.31
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.12/101.31
TERMS(mark(z0)) → c18(TERMS(z0)) 327.12/101.31
TERMS(ok(z0)) → c19(TERMS(z0)) 327.12/101.31
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.12/101.31
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.12/101.31
RECIP(mark(z0)) → c22(RECIP(z0)) 327.12/101.31
RECIP(ok(z0)) → c23(RECIP(z0)) 327.12/101.31
SQR(mark(z0)) → c24(SQR(z0)) 327.12/101.31
SQR(ok(z0)) → c25(SQR(z0)) 327.12/101.31
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.12/101.31
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.12/101.31
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.12/101.31
DBL(mark(z0)) → c29(DBL(z0)) 327.12/101.31
DBL(ok(z0)) → c30(DBL(z0)) 327.12/101.31
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.12/101.31
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.12/101.31
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.12/101.31
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.12/101.31
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.31
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.12/101.31
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.12/101.31
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.12/101.31
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.31
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.12/101.31
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.31
S(ok(z0)) → c44(S(z0)) 327.12/101.31
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.12/101.31
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.12/101.31
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.12/101.31
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.12/101.31
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.12/101.31
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.12/101.31
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.12/101.31
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.12/101.31
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.12/101.31
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.12/101.31
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.12/101.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.12/101.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.12/101.31
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.12/101.31
ACTIVE(terms(z0)) → c1(S(z0)) 327.12/101.31
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 327.12/101.31
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.31
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 327.12/101.31
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.31
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.31
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.31
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.31
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.31
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.31
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.31
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 327.12/101.31
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 327.12/101.31
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 327.12/101.31
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 327.12/101.31
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.12/101.31
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.12/101.31
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.12/101.31
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.12/101.31
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.12/101.31
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.12/101.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.12/101.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0)), ACTIVE(sqr(0))) 327.12/101.31
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.31
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 327.12/101.31
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.31
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.31
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.31
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.31
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.31
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.31
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.31
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0)), ACTIVE(sqr(0))) 327.12/101.31
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.31
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 327.12/101.31
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.31
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.31
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.31
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.31
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.31
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.31
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.31
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.31
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.31
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.12/101.31
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.12/101.31
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 327.12/101.31
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.12/101.31
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.12/101.31
TERMS(mark(z0)) → c18(TERMS(z0)) 327.12/101.31
TERMS(ok(z0)) → c19(TERMS(z0)) 327.12/101.31
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.12/101.31
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.12/101.31
RECIP(mark(z0)) → c22(RECIP(z0)) 327.12/101.31
RECIP(ok(z0)) → c23(RECIP(z0)) 327.12/101.31
SQR(mark(z0)) → c24(SQR(z0)) 327.12/101.31
SQR(ok(z0)) → c25(SQR(z0)) 327.12/101.31
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.12/101.31
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.12/101.31
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.12/101.31
DBL(mark(z0)) → c29(DBL(z0)) 327.12/101.31
DBL(ok(z0)) → c30(DBL(z0)) 327.12/101.31
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.12/101.31
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.12/101.31
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.12/101.31
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.12/101.31
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.31
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.12/101.31
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.12/101.31
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.12/101.31
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.31
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.12/101.31
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.31
S(ok(z0)) → c44(S(z0)) 327.12/101.31
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.12/101.31
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.12/101.31
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.12/101.31
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.12/101.31
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.12/101.31
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.12/101.31
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.12/101.31
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.12/101.31
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.12/101.31
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.12/101.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.12/101.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.12/101.31
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.12/101.31
ACTIVE(terms(z0)) → c1(S(z0)) 327.12/101.31
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 327.12/101.31
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.31
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 327.12/101.31
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.31
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.31
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.31
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.31
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.31
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.31
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.31
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 327.12/101.31
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 327.12/101.31
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 327.12/101.31
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 327.12/101.31
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.12/101.31
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.12/101.31
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.12/101.31
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.12/101.31
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.12/101.31
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.12/101.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.12/101.31
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.12/101.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.12/101.31
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0)), ACTIVE(sqr(0))) 327.12/101.31
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.31
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 327.12/101.31
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.31
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.31
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.31
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.31
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.31
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.31
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.39
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.39
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.39
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.39
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.39
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.39
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.39
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.39
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.39
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0)), ACTIVE(sqr(0))) 327.12/101.39
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.39
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 327.12/101.39
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.39
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.39
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.39
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.39
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.39
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.39
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.39
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.39
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.39
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.39
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.39
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.39
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.39
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

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, c1, c9, c10, c11, c12

327.12/101.39

(17) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 4 trailing tuple parts

327.12/101.39

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.12/101.39
active(sqr(0)) → mark(0) 327.12/101.39
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.12/101.39
active(dbl(0)) → mark(0) 327.12/101.39
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.12/101.39
active(add(0, z0)) → mark(z0) 327.12/101.39
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.12/101.39
active(first(0, z0)) → mark(nil) 327.12/101.39
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.12/101.39
active(terms(z0)) → terms(active(z0)) 327.12/101.39
active(cons(z0, z1)) → cons(active(z0), z1) 327.12/101.39
active(recip(z0)) → recip(active(z0)) 327.12/101.39
active(sqr(z0)) → sqr(active(z0)) 327.12/101.39
active(add(z0, z1)) → add(active(z0), z1) 327.12/101.39
active(add(z0, z1)) → add(z0, active(z1)) 327.12/101.39
active(dbl(z0)) → dbl(active(z0)) 327.12/101.39
active(first(z0, z1)) → first(active(z0), z1) 327.12/101.39
active(first(z0, z1)) → first(z0, active(z1)) 327.12/101.39
terms(mark(z0)) → mark(terms(z0)) 327.12/101.39
terms(ok(z0)) → ok(terms(z0)) 327.12/101.39
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.12/101.39
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.12/101.39
recip(mark(z0)) → mark(recip(z0)) 327.12/101.39
recip(ok(z0)) → ok(recip(z0)) 327.12/101.39
sqr(mark(z0)) → mark(sqr(z0)) 327.12/101.39
sqr(ok(z0)) → ok(sqr(z0)) 327.12/101.39
add(mark(z0), z1) → mark(add(z0, z1)) 327.12/101.39
add(z0, mark(z1)) → mark(add(z0, z1)) 327.12/101.39
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.12/101.39
dbl(mark(z0)) → mark(dbl(z0)) 327.12/101.39
dbl(ok(z0)) → ok(dbl(z0)) 327.12/101.39
first(mark(z0), z1) → mark(first(z0, z1)) 327.12/101.39
first(z0, mark(z1)) → mark(first(z0, z1)) 327.12/101.39
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.12/101.39
proper(terms(z0)) → terms(proper(z0)) 327.12/101.39
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.12/101.39
proper(recip(z0)) → recip(proper(z0)) 327.12/101.39
proper(sqr(z0)) → sqr(proper(z0)) 327.12/101.39
proper(s(z0)) → s(proper(z0)) 327.12/101.39
proper(0) → ok(0) 327.12/101.39
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.12/101.39
proper(dbl(z0)) → dbl(proper(z0)) 327.12/101.39
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.12/101.39
proper(nil) → ok(nil) 327.12/101.39
s(ok(z0)) → ok(s(z0)) 327.12/101.39
top(mark(z0)) → top(proper(z0)) 327.12/101.39
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.12/101.39
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.12/101.39
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 327.12/101.39
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.12/101.39
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.12/101.39
TERMS(mark(z0)) → c18(TERMS(z0)) 327.12/101.39
TERMS(ok(z0)) → c19(TERMS(z0)) 327.12/101.39
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.12/101.39
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.12/101.39
RECIP(mark(z0)) → c22(RECIP(z0)) 327.12/101.39
RECIP(ok(z0)) → c23(RECIP(z0)) 327.12/101.39
SQR(mark(z0)) → c24(SQR(z0)) 327.12/101.39
SQR(ok(z0)) → c25(SQR(z0)) 327.12/101.39
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.12/101.39
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.12/101.39
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.12/101.39
DBL(mark(z0)) → c29(DBL(z0)) 327.12/101.39
DBL(ok(z0)) → c30(DBL(z0)) 327.12/101.39
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.12/101.39
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.12/101.39
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.12/101.39
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.12/101.39
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.39
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.12/101.39
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.12/101.39
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.12/101.39
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.39
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.12/101.39
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.39
S(ok(z0)) → c44(S(z0)) 327.12/101.39
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.12/101.39
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.12/101.39
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.12/101.39
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.12/101.39
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.12/101.39
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.12/101.39
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.12/101.39
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.12/101.39
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.12/101.39
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.12/101.39
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.12/101.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.12/101.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.12/101.39
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.12/101.39
ACTIVE(terms(z0)) → c1(S(z0)) 327.12/101.39
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.39
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.39
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 327.12/101.39
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.39
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.39
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.39
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.39
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.39
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.39
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.39
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.39
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.39
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.39
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.39
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.39
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.39
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.39
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.12/101.39
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 327.12/101.39
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 327.12/101.39
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 327.12/101.39
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.12/101.39
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.12/101.39
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.12/101.39
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.39
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.12/101.39
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.12/101.39
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.12/101.39
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.12/101.39
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.12/101.39
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.12/101.39
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.12/101.39
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.12/101.39
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.12/101.39
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.39
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.39
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 327.12/101.39
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.39
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.39
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.39
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.39
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.39
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.12/101.40
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.12/101.40
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.12/101.40
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0)))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 327.12/101.40
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
TERMS(mark(z0)) → c18(TERMS(z0)) 327.12/101.40
TERMS(ok(z0)) → c19(TERMS(z0)) 327.12/101.40
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.12/101.40
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.12/101.40
RECIP(mark(z0)) → c22(RECIP(z0)) 327.12/101.40
RECIP(ok(z0)) → c23(RECIP(z0)) 327.12/101.40
SQR(mark(z0)) → c24(SQR(z0)) 327.12/101.40
SQR(ok(z0)) → c25(SQR(z0)) 327.12/101.40
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.12/101.40
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.12/101.40
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.12/101.40
DBL(mark(z0)) → c29(DBL(z0)) 327.12/101.40
DBL(ok(z0)) → c30(DBL(z0)) 327.12/101.40
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.12/101.40
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.12/101.40
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.12/101.40
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
S(ok(z0)) → c44(S(z0)) 327.12/101.40
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.12/101.40
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.12/101.40
ACTIVE(terms(z0)) → c1(S(z0)) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.12/101.40
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.12/101.40
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.12/101.40
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

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, c1, c9, c10, c11, c12, c9, c10, c11, c12

327.12/101.40

(19) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC

327.12/101.40

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.12/101.40
active(sqr(0)) → mark(0) 327.12/101.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.12/101.40
active(dbl(0)) → mark(0) 327.12/101.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.12/101.40
active(add(0, z0)) → mark(z0) 327.12/101.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.12/101.40
active(first(0, z0)) → mark(nil) 327.12/101.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.12/101.40
active(terms(z0)) → terms(active(z0)) 327.12/101.40
active(cons(z0, z1)) → cons(active(z0), z1) 327.12/101.40
active(recip(z0)) → recip(active(z0)) 327.12/101.40
active(sqr(z0)) → sqr(active(z0)) 327.12/101.40
active(add(z0, z1)) → add(active(z0), z1) 327.12/101.40
active(add(z0, z1)) → add(z0, active(z1)) 327.12/101.40
active(dbl(z0)) → dbl(active(z0)) 327.12/101.40
active(first(z0, z1)) → first(active(z0), z1) 327.12/101.40
active(first(z0, z1)) → first(z0, active(z1)) 327.12/101.40
terms(mark(z0)) → mark(terms(z0)) 327.12/101.40
terms(ok(z0)) → ok(terms(z0)) 327.12/101.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.12/101.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.12/101.40
recip(mark(z0)) → mark(recip(z0)) 327.12/101.40
recip(ok(z0)) → ok(recip(z0)) 327.12/101.40
sqr(mark(z0)) → mark(sqr(z0)) 327.12/101.40
sqr(ok(z0)) → ok(sqr(z0)) 327.12/101.40
add(mark(z0), z1) → mark(add(z0, z1)) 327.12/101.40
add(z0, mark(z1)) → mark(add(z0, z1)) 327.12/101.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.12/101.40
dbl(mark(z0)) → mark(dbl(z0)) 327.12/101.40
dbl(ok(z0)) → ok(dbl(z0)) 327.12/101.40
first(mark(z0), z1) → mark(first(z0, z1)) 327.12/101.40
first(z0, mark(z1)) → mark(first(z0, z1)) 327.12/101.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.12/101.40
proper(terms(z0)) → terms(proper(z0)) 327.12/101.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.12/101.40
proper(recip(z0)) → recip(proper(z0)) 327.12/101.40
proper(sqr(z0)) → sqr(proper(z0)) 327.12/101.40
proper(s(z0)) → s(proper(z0)) 327.12/101.40
proper(0) → ok(0) 327.12/101.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.12/101.40
proper(dbl(z0)) → dbl(proper(z0)) 327.12/101.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.12/101.40
proper(nil) → ok(nil) 327.12/101.40
s(ok(z0)) → ok(s(z0)) 327.12/101.40
top(mark(z0)) → top(proper(z0)) 327.12/101.40
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 327.12/101.40
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
TERMS(mark(z0)) → c18(TERMS(z0)) 327.12/101.40
TERMS(ok(z0)) → c19(TERMS(z0)) 327.12/101.40
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.12/101.40
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.12/101.40
RECIP(mark(z0)) → c22(RECIP(z0)) 327.12/101.40
RECIP(ok(z0)) → c23(RECIP(z0)) 327.12/101.40
SQR(mark(z0)) → c24(SQR(z0)) 327.12/101.40
SQR(ok(z0)) → c25(SQR(z0)) 327.12/101.40
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.12/101.40
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.12/101.40
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.12/101.40
DBL(mark(z0)) → c29(DBL(z0)) 327.12/101.40
DBL(ok(z0)) → c30(DBL(z0)) 327.12/101.40
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.12/101.40
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.12/101.40
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.12/101.40
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
S(ok(z0)) → c44(S(z0)) 327.12/101.40
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.12/101.40
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.12/101.40
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.12/101.40
ACTIVE(terms(z0)) → c1(S(z0)) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.12/101.40
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.12/101.40
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.12/101.40
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.12/101.40
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.12/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0))))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) 327.12/101.40
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
TERMS(mark(z0)) → c18(TERMS(z0)) 327.12/101.40
TERMS(ok(z0)) → c19(TERMS(z0)) 327.12/101.40
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.12/101.40
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.12/101.40
RECIP(mark(z0)) → c22(RECIP(z0)) 327.12/101.40
RECIP(ok(z0)) → c23(RECIP(z0)) 327.12/101.40
SQR(mark(z0)) → c24(SQR(z0)) 327.12/101.40
SQR(ok(z0)) → c25(SQR(z0)) 327.12/101.40
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.12/101.40
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.12/101.40
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.12/101.40
DBL(mark(z0)) → c29(DBL(z0)) 327.12/101.40
DBL(ok(z0)) → c30(DBL(z0)) 327.12/101.40
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.12/101.40
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.12/101.40
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.12/101.40
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
S(ok(z0)) → c44(S(z0)) 327.12/101.40
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.12/101.40
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.12/101.40
ACTIVE(terms(z0)) → c1(S(z0)) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.12/101.40
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.12/101.40
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.12/101.40
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.12/101.40
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.12/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0))))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

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, c1, c9, c10, c11, c12, c9, c10, c11, c12, c

327.12/101.40

(21) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace ACTIVE(dbl(z0)) → c15(DBL(active(z0)), ACTIVE(z0)) by

ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0)), ACTIVE(sqr(0))) 327.12/101.40
ACTIVE(dbl(sqr(s(z0)))) → c15(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(dbl(dbl(s(z0)))) → c15(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))

327.12/101.40

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.12/101.40
active(sqr(0)) → mark(0) 327.12/101.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.12/101.40
active(dbl(0)) → mark(0) 327.12/101.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.12/101.40
active(add(0, z0)) → mark(z0) 327.12/101.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.12/101.40
active(first(0, z0)) → mark(nil) 327.12/101.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.12/101.40
active(terms(z0)) → terms(active(z0)) 327.12/101.40
active(cons(z0, z1)) → cons(active(z0), z1) 327.12/101.40
active(recip(z0)) → recip(active(z0)) 327.12/101.40
active(sqr(z0)) → sqr(active(z0)) 327.12/101.40
active(add(z0, z1)) → add(active(z0), z1) 327.12/101.40
active(add(z0, z1)) → add(z0, active(z1)) 327.12/101.40
active(dbl(z0)) → dbl(active(z0)) 327.12/101.40
active(first(z0, z1)) → first(active(z0), z1) 327.12/101.40
active(first(z0, z1)) → first(z0, active(z1)) 327.12/101.40
terms(mark(z0)) → mark(terms(z0)) 327.12/101.40
terms(ok(z0)) → ok(terms(z0)) 327.12/101.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.12/101.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.12/101.40
recip(mark(z0)) → mark(recip(z0)) 327.12/101.40
recip(ok(z0)) → ok(recip(z0)) 327.12/101.40
sqr(mark(z0)) → mark(sqr(z0)) 327.12/101.40
sqr(ok(z0)) → ok(sqr(z0)) 327.12/101.40
add(mark(z0), z1) → mark(add(z0, z1)) 327.12/101.40
add(z0, mark(z1)) → mark(add(z0, z1)) 327.12/101.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.12/101.40
dbl(mark(z0)) → mark(dbl(z0)) 327.12/101.40
dbl(ok(z0)) → ok(dbl(z0)) 327.12/101.40
first(mark(z0), z1) → mark(first(z0, z1)) 327.12/101.40
first(z0, mark(z1)) → mark(first(z0, z1)) 327.12/101.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.12/101.40
proper(terms(z0)) → terms(proper(z0)) 327.12/101.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.12/101.40
proper(recip(z0)) → recip(proper(z0)) 327.12/101.40
proper(sqr(z0)) → sqr(proper(z0)) 327.12/101.40
proper(s(z0)) → s(proper(z0)) 327.12/101.40
proper(0) → ok(0) 327.12/101.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.12/101.40
proper(dbl(z0)) → dbl(proper(z0)) 327.12/101.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.12/101.40
proper(nil) → ok(nil) 327.12/101.40
s(ok(z0)) → ok(s(z0)) 327.12/101.40
top(mark(z0)) → top(proper(z0)) 327.12/101.40
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
TERMS(mark(z0)) → c18(TERMS(z0)) 327.12/101.40
TERMS(ok(z0)) → c19(TERMS(z0)) 327.12/101.40
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.12/101.40
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.12/101.40
RECIP(mark(z0)) → c22(RECIP(z0)) 327.12/101.40
RECIP(ok(z0)) → c23(RECIP(z0)) 327.12/101.40
SQR(mark(z0)) → c24(SQR(z0)) 327.12/101.40
SQR(ok(z0)) → c25(SQR(z0)) 327.12/101.40
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.12/101.40
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.12/101.40
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.12/101.40
DBL(mark(z0)) → c29(DBL(z0)) 327.12/101.40
DBL(ok(z0)) → c30(DBL(z0)) 327.12/101.40
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.12/101.40
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.12/101.40
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.12/101.40
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
S(ok(z0)) → c44(S(z0)) 327.12/101.40
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.12/101.40
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.12/101.40
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.12/101.40
ACTIVE(terms(z0)) → c1(S(z0)) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.12/101.40
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.12/101.40
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.12/101.40
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.12/101.40
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.12/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0)), ACTIVE(sqr(0))) 327.12/101.40
ACTIVE(dbl(sqr(s(z0)))) → c15(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(dbl(dbl(s(z0)))) → c15(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
TERMS(mark(z0)) → c18(TERMS(z0)) 327.12/101.40
TERMS(ok(z0)) → c19(TERMS(z0)) 327.12/101.40
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.12/101.40
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.12/101.40
RECIP(mark(z0)) → c22(RECIP(z0)) 327.12/101.40
RECIP(ok(z0)) → c23(RECIP(z0)) 327.12/101.40
SQR(mark(z0)) → c24(SQR(z0)) 327.12/101.40
SQR(ok(z0)) → c25(SQR(z0)) 327.12/101.40
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.12/101.40
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.12/101.40
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.12/101.40
DBL(mark(z0)) → c29(DBL(z0)) 327.12/101.40
DBL(ok(z0)) → c30(DBL(z0)) 327.12/101.40
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.12/101.40
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.12/101.40
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.12/101.40
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
S(ok(z0)) → c44(S(z0)) 327.12/101.40
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.12/101.40
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.12/101.40
ACTIVE(terms(z0)) → c1(S(z0)) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.12/101.40
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.12/101.40
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.12/101.40
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.12/101.40
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.12/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.12/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0)), ACTIVE(sqr(0))) 327.12/101.40
ACTIVE(dbl(sqr(s(z0)))) → c15(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.12/101.40
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0)), ACTIVE(dbl(0))) 327.12/101.40
ACTIVE(dbl(dbl(s(z0)))) → c15(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, 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, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15

327.12/101.40

(23) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 6 trailing tuple parts

327.12/101.40

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.12/101.40
active(sqr(0)) → mark(0) 327.12/101.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.12/101.40
active(dbl(0)) → mark(0) 327.12/101.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.12/101.40
active(add(0, z0)) → mark(z0) 327.12/101.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.12/101.40
active(first(0, z0)) → mark(nil) 327.12/101.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.12/101.40
active(terms(z0)) → terms(active(z0)) 327.12/101.40
active(cons(z0, z1)) → cons(active(z0), z1) 327.12/101.40
active(recip(z0)) → recip(active(z0)) 327.12/101.40
active(sqr(z0)) → sqr(active(z0)) 327.12/101.40
active(add(z0, z1)) → add(active(z0), z1) 327.12/101.40
active(add(z0, z1)) → add(z0, active(z1)) 327.12/101.40
active(dbl(z0)) → dbl(active(z0)) 327.12/101.40
active(first(z0, z1)) → first(active(z0), z1) 327.12/101.40
active(first(z0, z1)) → first(z0, active(z1)) 327.12/101.40
terms(mark(z0)) → mark(terms(z0)) 327.12/101.40
terms(ok(z0)) → ok(terms(z0)) 327.12/101.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.12/101.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.12/101.40
recip(mark(z0)) → mark(recip(z0)) 327.12/101.40
recip(ok(z0)) → ok(recip(z0)) 327.12/101.40
sqr(mark(z0)) → mark(sqr(z0)) 327.12/101.40
sqr(ok(z0)) → ok(sqr(z0)) 327.12/101.40
add(mark(z0), z1) → mark(add(z0, z1)) 327.12/101.40
add(z0, mark(z1)) → mark(add(z0, z1)) 327.12/101.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.12/101.40
dbl(mark(z0)) → mark(dbl(z0)) 327.12/101.40
dbl(ok(z0)) → ok(dbl(z0)) 327.12/101.40
first(mark(z0), z1) → mark(first(z0, z1)) 327.12/101.40
first(z0, mark(z1)) → mark(first(z0, z1)) 327.12/101.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.12/101.40
proper(terms(z0)) → terms(proper(z0)) 327.12/101.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.12/101.40
proper(recip(z0)) → recip(proper(z0)) 327.12/101.40
proper(sqr(z0)) → sqr(proper(z0)) 327.12/101.40
proper(s(z0)) → s(proper(z0)) 327.12/101.40
proper(0) → ok(0) 327.12/101.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.12/101.40
proper(dbl(z0)) → dbl(proper(z0)) 327.12/101.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.12/101.40
proper(nil) → ok(nil) 327.12/101.40
s(ok(z0)) → ok(s(z0)) 327.12/101.40
top(mark(z0)) → top(proper(z0)) 327.12/101.40
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.12/101.40
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.12/101.40
TERMS(mark(z0)) → c18(TERMS(z0)) 327.12/101.40
TERMS(ok(z0)) → c19(TERMS(z0)) 327.12/101.40
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.12/101.40
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.12/101.40
RECIP(mark(z0)) → c22(RECIP(z0)) 327.12/101.40
RECIP(ok(z0)) → c23(RECIP(z0)) 327.12/101.40
SQR(mark(z0)) → c24(SQR(z0)) 327.12/101.40
SQR(ok(z0)) → c25(SQR(z0)) 327.12/101.40
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.12/101.40
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.12/101.40
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.12/101.40
DBL(mark(z0)) → c29(DBL(z0)) 327.12/101.40
DBL(ok(z0)) → c30(DBL(z0)) 327.12/101.40
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.12/101.40
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.12/101.40
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.12/101.40
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.12/101.40
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.12/101.40
S(ok(z0)) → c44(S(z0)) 327.12/101.40
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.12/101.40
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.12/101.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.12/101.40
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.12/101.40
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.12/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.12/101.40
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.12/101.40
ACTIVE(terms(z0)) → c1(S(z0)) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.12/101.40
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.12/101.40
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.12/101.40
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.12/101.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.12/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.12/101.40
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.12/101.40
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.12/101.40
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.12/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.12/101.40
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.40
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.40
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.40
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.40
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.40
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.40
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(dbl(sqr(s(z0)))) → c15(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(dbl(dbl(s(z0)))) → c15(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.40
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.40
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.40
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.40
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.40
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0)))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.40
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.40
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.40
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.40
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.40
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.40
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.40
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.40
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.40
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.40
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.40
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.40
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.40
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.40
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.40
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.40
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.40
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.40
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.40
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.40
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.46/101.40
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.40
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.46/101.40
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.40
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.40
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.40
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.40
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.40
S(ok(z0)) → c44(S(z0)) 327.46/101.40
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.40
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.40
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.40
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.40
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.40
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.40
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.40
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.40
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.40
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.40
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.40
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.40
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.40
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.40
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.40
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(dbl(sqr(s(z0)))) → c15(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(dbl(dbl(s(z0)))) → c15(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.40
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.40
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.40
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.40
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.40
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, 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, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15

327.46/101.40

(25) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC

327.46/101.40

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.40
active(sqr(0)) → mark(0) 327.46/101.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.40
active(dbl(0)) → mark(0) 327.46/101.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.40
active(add(0, z0)) → mark(z0) 327.46/101.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.40
active(first(0, z0)) → mark(nil) 327.46/101.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.40
active(terms(z0)) → terms(active(z0)) 327.46/101.40
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.40
active(recip(z0)) → recip(active(z0)) 327.46/101.40
active(sqr(z0)) → sqr(active(z0)) 327.46/101.40
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.40
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.40
active(dbl(z0)) → dbl(active(z0)) 327.46/101.40
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.40
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.40
terms(mark(z0)) → mark(terms(z0)) 327.46/101.40
terms(ok(z0)) → ok(terms(z0)) 327.46/101.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.40
recip(mark(z0)) → mark(recip(z0)) 327.46/101.40
recip(ok(z0)) → ok(recip(z0)) 327.46/101.40
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.40
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.40
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.40
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.40
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.40
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.40
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.40
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.40
proper(terms(z0)) → terms(proper(z0)) 327.46/101.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.40
proper(recip(z0)) → recip(proper(z0)) 327.46/101.40
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.40
proper(s(z0)) → s(proper(z0)) 327.46/101.40
proper(0) → ok(0) 327.46/101.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.40
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.40
proper(nil) → ok(nil) 327.46/101.40
s(ok(z0)) → ok(s(z0)) 327.46/101.40
top(mark(z0)) → top(proper(z0)) 327.46/101.40
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.40
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.40
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.40
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.40
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.40
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.40
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.40
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.40
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.40
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.40
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.40
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.40
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.40
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.40
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.40
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.40
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.40
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.40
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.40
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.40
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.46/101.40
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.40
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.46/101.40
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.40
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.40
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.40
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.40
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.40
S(ok(z0)) → c44(S(z0)) 327.46/101.40
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.40
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.40
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.40
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.40
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.40
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.40
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.40
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.40
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.40
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.40
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.40
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.40
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.40
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.40
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.40
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.40
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.40
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.40
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.40
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.40
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.40
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.40
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.40
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.40
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.40
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.40
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.40
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.40
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.40
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.40
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.40
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.40
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.40
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.40
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.40
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.40
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.40
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.40
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.40
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.40
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.40
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.40
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.40
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.40
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.40
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.40
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.40
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.41
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.41
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.41
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.41
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.41
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.41
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.41
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.41
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.41
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.41
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.41
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.41
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.41
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.41
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.41
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.41
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.41
PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
S(ok(z0)) → c44(S(z0)) 327.46/101.41
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.41
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.41
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.41
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0))))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, 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, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2

327.46/101.41

(27) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(terms(z0)) → c34(TERMS(proper(z0)), PROPER(z0)) by

PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.41
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.41
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.41
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.41
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.41
PROPER(terms(0)) → c34(TERMS(ok(0)), PROPER(0)) 327.46/101.41
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.41
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.41
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.41
PROPER(terms(nil)) → c34(TERMS(ok(nil)), PROPER(nil))

327.46/101.41

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.41
active(sqr(0)) → mark(0) 327.46/101.41
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.41
active(dbl(0)) → mark(0) 327.46/101.41
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.41
active(add(0, z0)) → mark(z0) 327.46/101.41
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.41
active(first(0, z0)) → mark(nil) 327.46/101.41
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.41
active(terms(z0)) → terms(active(z0)) 327.46/101.41
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.41
active(recip(z0)) → recip(active(z0)) 327.46/101.41
active(sqr(z0)) → sqr(active(z0)) 327.46/101.41
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.41
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.41
active(dbl(z0)) → dbl(active(z0)) 327.46/101.41
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.41
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.41
terms(mark(z0)) → mark(terms(z0)) 327.46/101.41
terms(ok(z0)) → ok(terms(z0)) 327.46/101.41
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.41
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.41
recip(mark(z0)) → mark(recip(z0)) 327.46/101.41
recip(ok(z0)) → ok(recip(z0)) 327.46/101.41
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.41
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.41
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.41
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.41
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.41
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.41
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.41
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.41
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.41
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.41
proper(terms(z0)) → terms(proper(z0)) 327.46/101.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.41
proper(recip(z0)) → recip(proper(z0)) 327.46/101.41
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.41
proper(s(z0)) → s(proper(z0)) 327.46/101.41
proper(0) → ok(0) 327.46/101.41
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.41
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.41
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.41
proper(nil) → ok(nil) 327.46/101.41
s(ok(z0)) → ok(s(z0)) 327.46/101.41
top(mark(z0)) → top(proper(z0)) 327.46/101.41
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.41
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.41
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.41
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.41
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.41
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.41
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.41
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.41
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.41
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.41
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.41
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.41
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.41
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.41
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.41
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.41
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.41
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.41
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.41
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.41
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
S(ok(z0)) → c44(S(z0)) 327.46/101.41
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.41
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.41
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.41
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.41
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.41
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.41
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.41
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.41
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.41
PROPER(terms(0)) → c34(TERMS(ok(0)), PROPER(0)) 327.46/101.41
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.41
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.41
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.41
PROPER(terms(nil)) → c34(TERMS(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.41
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.41
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.41
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.41
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.41
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.41
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.41
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.41
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.41
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.41
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.41
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.41
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.41
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.41
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.41
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.41
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.41
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.41
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.41
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.41
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
S(ok(z0)) → c44(S(z0)) 327.46/101.41
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.41
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.41
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.41
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.41
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.41
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.41
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.41
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.41
PROPER(terms(0)) → c34(TERMS(ok(0)), PROPER(0)) 327.46/101.41
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.41
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.41
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.41
PROPER(terms(nil)) → c34(TERMS(ok(nil)), PROPER(nil))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c40, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34

327.46/101.41

(29) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

327.46/101.41

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.41
active(sqr(0)) → mark(0) 327.46/101.41
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.41
active(dbl(0)) → mark(0) 327.46/101.41
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.41
active(add(0, z0)) → mark(z0) 327.46/101.41
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.41
active(first(0, z0)) → mark(nil) 327.46/101.41
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.41
active(terms(z0)) → terms(active(z0)) 327.46/101.41
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.41
active(recip(z0)) → recip(active(z0)) 327.46/101.41
active(sqr(z0)) → sqr(active(z0)) 327.46/101.41
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.41
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.41
active(dbl(z0)) → dbl(active(z0)) 327.46/101.41
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.41
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.41
terms(mark(z0)) → mark(terms(z0)) 327.46/101.41
terms(ok(z0)) → ok(terms(z0)) 327.46/101.41
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.41
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.41
recip(mark(z0)) → mark(recip(z0)) 327.46/101.41
recip(ok(z0)) → ok(recip(z0)) 327.46/101.41
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.41
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.41
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.41
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.41
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.41
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.41
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.41
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.41
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.41
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.41
proper(terms(z0)) → terms(proper(z0)) 327.46/101.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.41
proper(recip(z0)) → recip(proper(z0)) 327.46/101.41
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.41
proper(s(z0)) → s(proper(z0)) 327.46/101.41
proper(0) → ok(0) 327.46/101.41
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.41
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.41
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.41
proper(nil) → ok(nil) 327.46/101.41
s(ok(z0)) → ok(s(z0)) 327.46/101.41
top(mark(z0)) → top(proper(z0)) 327.46/101.41
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.41
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.41
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.41
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.41
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.41
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.41
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.41
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.41
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.41
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.41
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.41
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.41
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.41
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.41
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.41
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.41
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.41
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.41
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.41
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.41
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
S(ok(z0)) → c44(S(z0)) 327.46/101.41
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.41
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.41
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.41
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.41
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.41
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.41
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.41
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.41
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.41
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.41
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.41
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.41
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.41
PROPER(terms(nil)) → c34(TERMS(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.41
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.41
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.41
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.41
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.41
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.41
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.41
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.41
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.41
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.41
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.41
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.41
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.41
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.41
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.41
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.41
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.41
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.41
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.41
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.41
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
S(ok(z0)) → c44(S(z0)) 327.46/101.41
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.41
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.41
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.41
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.41
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.41
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.41
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.41
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.41
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.41
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.41
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.41
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.41
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.41
PROPER(terms(nil)) → c34(TERMS(ok(nil)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c40, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34

327.46/101.41

(31) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.41
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.41
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.41
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.41
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.41
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 327.46/101.41
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.41
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.41
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.41
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 327.46/101.41
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.41
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.41
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.41
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.41
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.41
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 327.46/101.41
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.41
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.41
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.41
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

327.46/101.41

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.41
active(sqr(0)) → mark(0) 327.46/101.41
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.41
active(dbl(0)) → mark(0) 327.46/101.41
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.41
active(add(0, z0)) → mark(z0) 327.46/101.41
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.41
active(first(0, z0)) → mark(nil) 327.46/101.41
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.41
active(terms(z0)) → terms(active(z0)) 327.46/101.41
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.41
active(recip(z0)) → recip(active(z0)) 327.46/101.41
active(sqr(z0)) → sqr(active(z0)) 327.46/101.41
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.41
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.41
active(dbl(z0)) → dbl(active(z0)) 327.46/101.41
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.41
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.41
terms(mark(z0)) → mark(terms(z0)) 327.46/101.41
terms(ok(z0)) → ok(terms(z0)) 327.46/101.41
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.41
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.41
recip(mark(z0)) → mark(recip(z0)) 327.46/101.41
recip(ok(z0)) → ok(recip(z0)) 327.46/101.41
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.41
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.41
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.41
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.41
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.41
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.41
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.41
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.41
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.41
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.41
proper(terms(z0)) → terms(proper(z0)) 327.46/101.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.41
proper(recip(z0)) → recip(proper(z0)) 327.46/101.41
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.41
proper(s(z0)) → s(proper(z0)) 327.46/101.41
proper(0) → ok(0) 327.46/101.41
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.41
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.41
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.41
proper(nil) → ok(nil) 327.46/101.41
s(ok(z0)) → ok(s(z0)) 327.46/101.41
top(mark(z0)) → top(proper(z0)) 327.46/101.41
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.41
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.41
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.41
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.41
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.41
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.41
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.41
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.41
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.41
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.41
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.41
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.41
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.41
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.41
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.41
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.41
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.41
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.41
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.41
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.41
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.41
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.41
S(ok(z0)) → c44(S(z0)) 327.46/101.41
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.41
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.41
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.41
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.41
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.41
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.41
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.41
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.41
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.41
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.41
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.41
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.41
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.41
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.41
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.41
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.41
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.41
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.41
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.41
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.41
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.41
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.41
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.41
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.43
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.43
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.43
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.43
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.43
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.43
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.43
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.43
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.43
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.43
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.43
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.43
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.43
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.43
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.43
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.43
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.43
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.43
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.43
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.43
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.43
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.43
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.43
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.43
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.43
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.43
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 327.46/101.43
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.43
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.43
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.43
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 327.46/101.43
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.43
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.43
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.43
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.43
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.43
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 327.46/101.43
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.43
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.43
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.43
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.43
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.43
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.43
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.43
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.44
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.44
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.44
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.44
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.44
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.44
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.44
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.44
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.44
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.44
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.44
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.44
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.44
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.44
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.44
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.44
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.44
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.44
S(ok(z0)) → c44(S(z0)) 327.46/101.44
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.44
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.44
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.44
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.44
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.44
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.44
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.44
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.44
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.44
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.44
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.44
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.44
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.44
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.44
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.44
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.44
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.44
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.44
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.44
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.44
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.44
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.44
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.44
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.44
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.44
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.44
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.44
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.44
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.44
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.44
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.44
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.44
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.44
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.44
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 327.46/101.44
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.44
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.44
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.44
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 327.46/101.44
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.44
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 327.46/101.44
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.44
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.44
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c36, c37, c38, c40, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35

327.46/101.44

(33) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 4 trailing tuple parts

327.46/101.44

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.44
active(sqr(0)) → mark(0) 327.46/101.44
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.44
active(dbl(0)) → mark(0) 327.46/101.44
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.44
active(add(0, z0)) → mark(z0) 327.46/101.44
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.44
active(first(0, z0)) → mark(nil) 327.46/101.44
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.44
active(terms(z0)) → terms(active(z0)) 327.46/101.44
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.44
active(recip(z0)) → recip(active(z0)) 327.46/101.44
active(sqr(z0)) → sqr(active(z0)) 327.46/101.44
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.44
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.44
active(dbl(z0)) → dbl(active(z0)) 327.46/101.44
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.44
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.44
terms(mark(z0)) → mark(terms(z0)) 327.46/101.44
terms(ok(z0)) → ok(terms(z0)) 327.46/101.44
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.44
recip(mark(z0)) → mark(recip(z0)) 327.46/101.44
recip(ok(z0)) → ok(recip(z0)) 327.46/101.44
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.44
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.44
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.44
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.44
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.44
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.44
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.44
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.44
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.44
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.44
proper(terms(z0)) → terms(proper(z0)) 327.46/101.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.44
proper(recip(z0)) → recip(proper(z0)) 327.46/101.44
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.44
proper(s(z0)) → s(proper(z0)) 327.46/101.44
proper(0) → ok(0) 327.46/101.44
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.44
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.44
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.44
proper(nil) → ok(nil) 327.46/101.44
s(ok(z0)) → ok(s(z0)) 327.46/101.44
top(mark(z0)) → top(proper(z0)) 327.46/101.44
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.44
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.44
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.44
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.44
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.44
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.44
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.44
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.44
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.44
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.44
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.44
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.44
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.44
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.44
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.44
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.44
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.44
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.44
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.44
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.44
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.44
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.44
S(ok(z0)) → c44(S(z0)) 327.46/101.44
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.44
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.44
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.44
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.44
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.44
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.44
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.44
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.44
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.44
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.44
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.44
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.44
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.44
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.44
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.44
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.44
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.44
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.44
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.44
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.44
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.44
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.44
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.44
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.44
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.44
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.44
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.44
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.44
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.44
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.44
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.44
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.44
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.44
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.44
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.44
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.44
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.44
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.44
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.44
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.44
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.44
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.44
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.44
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.44
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.44
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.44
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.44
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.44
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.44
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.44
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.44
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.44
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.44
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.44
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.44
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.44
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.44
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.44
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.44
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.44
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.44
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.44
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.44
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.44
PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.44
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.44
S(ok(z0)) → c44(S(z0)) 327.46/101.44
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.44
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.44
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.44
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.44
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.44
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.44
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.44
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.44
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.44
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.44
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.44
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.44
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.44
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.44
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.44
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.44
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.44
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.44
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.44
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.44
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.44
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.44
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.44
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.44
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.44
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.44
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.44
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.44
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.44
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.44
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.44
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.44
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.44
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.44
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.44
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.44
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.44
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.44
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.44
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.44
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.44
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.44
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.44
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.44
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.44
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.44
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.44
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.44
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c36, c37, c38, c40, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35

327.46/101.44

(35) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(recip(z0)) → c36(RECIP(proper(z0)), PROPER(z0)) by

PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.44
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.44
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.44
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.44
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.44
PROPER(recip(0)) → c36(RECIP(ok(0)), PROPER(0)) 327.46/101.44
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.44
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.44
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.44
PROPER(recip(nil)) → c36(RECIP(ok(nil)), PROPER(nil))

327.46/101.44

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.44
active(sqr(0)) → mark(0) 327.46/101.44
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.44
active(dbl(0)) → mark(0) 327.46/101.44
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.44
active(add(0, z0)) → mark(z0) 327.46/101.44
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.44
active(first(0, z0)) → mark(nil) 327.46/101.44
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.44
active(terms(z0)) → terms(active(z0)) 327.46/101.44
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.44
active(recip(z0)) → recip(active(z0)) 327.46/101.44
active(sqr(z0)) → sqr(active(z0)) 327.46/101.44
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.44
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.44
active(dbl(z0)) → dbl(active(z0)) 327.46/101.44
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.44
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.44
terms(mark(z0)) → mark(terms(z0)) 327.46/101.44
terms(ok(z0)) → ok(terms(z0)) 327.46/101.44
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.44
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.44
recip(mark(z0)) → mark(recip(z0)) 327.46/101.44
recip(ok(z0)) → ok(recip(z0)) 327.46/101.44
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.44
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.44
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.44
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.44
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.44
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.44
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.44
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.44
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.44
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.44
proper(terms(z0)) → terms(proper(z0)) 327.46/101.44
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.44
proper(recip(z0)) → recip(proper(z0)) 327.46/101.44
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.44
proper(s(z0)) → s(proper(z0)) 327.46/101.44
proper(0) → ok(0) 327.46/101.44
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.44
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.44
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.44
proper(nil) → ok(nil) 327.46/101.44
s(ok(z0)) → ok(s(z0)) 327.46/101.44
top(mark(z0)) → top(proper(z0)) 327.46/101.44
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.44
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.44
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.44
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.44
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.44
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.44
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.44
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.44
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.44
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.44
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.44
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.44
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.44
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.44
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.44
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.44
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.44
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.44
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.44
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.44
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.44
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.44
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.44
S(ok(z0)) → c44(S(z0)) 327.46/101.44
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.44
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.44
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.44
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.44
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.44
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.44
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.44
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.44
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.44
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.44
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.44
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.44
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.44
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.44
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.44
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.44
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.44
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.44
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.44
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.44
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.44
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.45
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.45
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.45
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.45
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.45
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.45
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.45
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.45
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.45
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.45
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.45
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(recip(0)) → c36(RECIP(ok(0)), PROPER(0)) 327.46/101.45
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(recip(nil)) → c36(RECIP(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.45
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.45
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.45
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.45
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.45
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.45
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.45
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.45
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.45
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.45
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.45
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.45
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.45
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.45
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.45
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.45
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
S(ok(z0)) → c44(S(z0)) 327.46/101.45
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.45
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.45
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.45
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.45
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.45
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.45
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.45
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.45
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.45
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.45
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.45
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.45
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.45
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(recip(0)) → c36(RECIP(ok(0)), PROPER(0)) 327.46/101.45
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(recip(nil)) → c36(RECIP(ok(nil)), PROPER(nil))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c37, c38, c40, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36

327.46/101.45

(37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

327.46/101.45

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.45
active(sqr(0)) → mark(0) 327.46/101.45
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.45
active(dbl(0)) → mark(0) 327.46/101.45
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.45
active(add(0, z0)) → mark(z0) 327.46/101.45
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.45
active(first(0, z0)) → mark(nil) 327.46/101.45
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.45
active(terms(z0)) → terms(active(z0)) 327.46/101.45
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.45
active(recip(z0)) → recip(active(z0)) 327.46/101.45
active(sqr(z0)) → sqr(active(z0)) 327.46/101.45
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.45
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.45
active(dbl(z0)) → dbl(active(z0)) 327.46/101.45
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.45
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.45
terms(mark(z0)) → mark(terms(z0)) 327.46/101.45
terms(ok(z0)) → ok(terms(z0)) 327.46/101.45
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.45
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.45
recip(mark(z0)) → mark(recip(z0)) 327.46/101.45
recip(ok(z0)) → ok(recip(z0)) 327.46/101.45
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.45
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.45
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.45
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.45
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.45
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.45
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.45
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.45
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.45
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.45
proper(terms(z0)) → terms(proper(z0)) 327.46/101.45
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.45
proper(recip(z0)) → recip(proper(z0)) 327.46/101.45
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.45
proper(s(z0)) → s(proper(z0)) 327.46/101.45
proper(0) → ok(0) 327.46/101.45
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.45
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.45
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.45
proper(nil) → ok(nil) 327.46/101.45
s(ok(z0)) → ok(s(z0)) 327.46/101.45
top(mark(z0)) → top(proper(z0)) 327.46/101.45
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.45
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.45
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.45
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.45
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.45
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.45
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.45
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.45
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.45
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.45
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.45
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.45
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.45
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.45
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.45
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.45
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
S(ok(z0)) → c44(S(z0)) 327.46/101.45
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.45
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.45
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.45
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.45
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.45
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.45
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.45
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.45
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.45
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.45
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.45
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.45
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.45
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.45
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.46/101.45
PROPER(recip(nil)) → c36(RECIP(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.45
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.45
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.45
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.45
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.45
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.45
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.45
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.45
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.45
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.45
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.45
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.45
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.45
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.45
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.45
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.45
PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
S(ok(z0)) → c44(S(z0)) 327.46/101.45
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.45
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.45
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.45
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.45
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.45
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.45
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.45
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.45
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.45
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.45
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.45
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.45
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.45
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.46/101.45
PROPER(recip(nil)) → c36(RECIP(ok(nil)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c37, c38, c40, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36

327.46/101.45

(39) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(sqr(z0)) → c37(SQR(proper(z0)), PROPER(z0)) by

PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(sqr(0)) → c37(SQR(ok(0)), PROPER(0)) 327.46/101.45
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(sqr(nil)) → c37(SQR(ok(nil)), PROPER(nil))

327.46/101.45

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.45
active(sqr(0)) → mark(0) 327.46/101.45
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.45
active(dbl(0)) → mark(0) 327.46/101.45
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.45
active(add(0, z0)) → mark(z0) 327.46/101.45
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.45
active(first(0, z0)) → mark(nil) 327.46/101.45
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.45
active(terms(z0)) → terms(active(z0)) 327.46/101.45
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.45
active(recip(z0)) → recip(active(z0)) 327.46/101.45
active(sqr(z0)) → sqr(active(z0)) 327.46/101.45
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.45
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.45
active(dbl(z0)) → dbl(active(z0)) 327.46/101.45
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.45
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.45
terms(mark(z0)) → mark(terms(z0)) 327.46/101.45
terms(ok(z0)) → ok(terms(z0)) 327.46/101.45
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.45
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.45
recip(mark(z0)) → mark(recip(z0)) 327.46/101.45
recip(ok(z0)) → ok(recip(z0)) 327.46/101.45
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.45
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.45
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.45
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.45
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.45
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.45
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.45
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.45
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.45
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.45
proper(terms(z0)) → terms(proper(z0)) 327.46/101.45
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.45
proper(recip(z0)) → recip(proper(z0)) 327.46/101.45
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.45
proper(s(z0)) → s(proper(z0)) 327.46/101.45
proper(0) → ok(0) 327.46/101.45
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.45
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.45
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.45
proper(nil) → ok(nil) 327.46/101.45
s(ok(z0)) → ok(s(z0)) 327.46/101.45
top(mark(z0)) → top(proper(z0)) 327.46/101.45
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.45
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.45
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.45
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.45
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.45
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.45
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.45
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.45
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.45
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.45
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.45
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.45
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.45
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.45
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.45
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.45
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
S(ok(z0)) → c44(S(z0)) 327.46/101.45
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.45
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.45
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.45
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.45
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.45
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.45
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.45
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.45
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.45
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.45
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.45
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.45
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.45
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.45
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.46/101.45
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.46/101.45
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(sqr(0)) → c37(SQR(ok(0)), PROPER(0)) 327.46/101.45
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(sqr(nil)) → c37(SQR(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.45
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.45
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.45
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.45
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.45
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.45
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.45
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.45
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.45
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.45
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.45
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.45
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.45
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.45
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.45
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.45
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
S(ok(z0)) → c44(S(z0)) 327.46/101.45
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.45
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.45
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.45
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.45
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.45
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.45
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.45
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.45
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.45
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.45
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.45
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.45
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.45
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.45
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.45
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.45
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.45
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.45
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.46/101.45
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.46/101.45
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.45
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.45
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.45
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.45
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.46/101.45
PROPER(sqr(0)) → c37(SQR(ok(0)), PROPER(0)) 327.46/101.45
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.45
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.45
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.45
PROPER(sqr(nil)) → c37(SQR(ok(nil)), PROPER(nil))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c38, c40, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37

327.46/101.45

(41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

327.46/101.45

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.45
active(sqr(0)) → mark(0) 327.46/101.45
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.45
active(dbl(0)) → mark(0) 327.46/101.45
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.45
active(add(0, z0)) → mark(z0) 327.46/101.45
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.45
active(first(0, z0)) → mark(nil) 327.46/101.45
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.45
active(terms(z0)) → terms(active(z0)) 327.46/101.45
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.45
active(recip(z0)) → recip(active(z0)) 327.46/101.45
active(sqr(z0)) → sqr(active(z0)) 327.46/101.45
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.45
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.45
active(dbl(z0)) → dbl(active(z0)) 327.46/101.45
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.45
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.45
terms(mark(z0)) → mark(terms(z0)) 327.46/101.45
terms(ok(z0)) → ok(terms(z0)) 327.46/101.45
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.45
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.45
recip(mark(z0)) → mark(recip(z0)) 327.46/101.45
recip(ok(z0)) → ok(recip(z0)) 327.46/101.45
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.45
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.45
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.45
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.45
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.45
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.45
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.45
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.45
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.45
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.45
proper(terms(z0)) → terms(proper(z0)) 327.46/101.45
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.45
proper(recip(z0)) → recip(proper(z0)) 327.46/101.45
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.45
proper(s(z0)) → s(proper(z0)) 327.46/101.45
proper(0) → ok(0) 327.46/101.45
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.45
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.45
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.45
proper(nil) → ok(nil) 327.46/101.45
s(ok(z0)) → ok(s(z0)) 327.46/101.45
top(mark(z0)) → top(proper(z0)) 327.46/101.45
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.45
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.45
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.45
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.45
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.45
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.45
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.45
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.45
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.45
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.45
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.45
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.45
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.45
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.45
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.45
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.45
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.45
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.45
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.45
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.45
S(ok(z0)) → c44(S(z0)) 327.46/101.45
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.45
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.45
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.45
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.45
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.45
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.45
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.45
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.45
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.45
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.45
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.45
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.45
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.45
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.45
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.45
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.45
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.45
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.45
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.45
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.45
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.45
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.45
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.45
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.46
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.46
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.46
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.46
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.46
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.46
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.46
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.46
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.46
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.46
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.46
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.46
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.46
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.46
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.46
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.46/101.46
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.46/101.46
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.46/101.46
PROPER(sqr(nil)) → c37(SQR(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.46
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.46
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.46
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.46
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.46
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.46
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.46
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.46
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.46
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.46
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.46
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.46
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.46
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.46
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.46
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.46
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.46
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.46
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.46
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.46
PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) 327.46/101.46
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.46
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.46
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.46
S(ok(z0)) → c44(S(z0)) 327.46/101.46
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.46
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.46
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.46
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.46
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.46
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.46
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.46
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.46
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.46
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.46
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.46
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.46
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.46
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.46
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.46
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.46
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.46
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.46
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.46
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.46
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.46
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.46
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.46
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.46
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.46
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.46
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.46
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.46
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.46
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.46
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.46
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.46
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.46
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.46
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.46
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.46/101.46
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.46/101.46
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.46/101.46
PROPER(sqr(nil)) → c37(SQR(ok(nil)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c38, c40, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37

327.46/101.46

(43) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(s(z0)) → c38(S(proper(z0)), PROPER(z0)) by

PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(s(0)) → c38(S(ok(0)), PROPER(0)) 327.46/101.46
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(s(nil)) → c38(S(ok(nil)), PROPER(nil))

327.46/101.46

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.46
active(sqr(0)) → mark(0) 327.46/101.46
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.46
active(dbl(0)) → mark(0) 327.46/101.46
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.46
active(add(0, z0)) → mark(z0) 327.46/101.46
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.46
active(first(0, z0)) → mark(nil) 327.46/101.46
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.46
active(terms(z0)) → terms(active(z0)) 327.46/101.46
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.46
active(recip(z0)) → recip(active(z0)) 327.46/101.46
active(sqr(z0)) → sqr(active(z0)) 327.46/101.46
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.46
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.46
active(dbl(z0)) → dbl(active(z0)) 327.46/101.46
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.46
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.46
terms(mark(z0)) → mark(terms(z0)) 327.46/101.46
terms(ok(z0)) → ok(terms(z0)) 327.46/101.46
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.46
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.46
recip(mark(z0)) → mark(recip(z0)) 327.46/101.46
recip(ok(z0)) → ok(recip(z0)) 327.46/101.46
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.46
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.46
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.46
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.46
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.46
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.46
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.46
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.46
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.46
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.46
proper(terms(z0)) → terms(proper(z0)) 327.46/101.46
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.46
proper(recip(z0)) → recip(proper(z0)) 327.46/101.46
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.46
proper(s(z0)) → s(proper(z0)) 327.46/101.46
proper(0) → ok(0) 327.46/101.46
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.46
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.46
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.46
proper(nil) → ok(nil) 327.46/101.46
s(ok(z0)) → ok(s(z0)) 327.46/101.46
top(mark(z0)) → top(proper(z0)) 327.46/101.46
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.46
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.46
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.46
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.46
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.46
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.46
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.46
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.46
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.46
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.46
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.46
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.46
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.46
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.46
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.46
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.46
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.46
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.46
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.46
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.46
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.46
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.46
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.46
S(ok(z0)) → c44(S(z0)) 327.46/101.46
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.46
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.46
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.46
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.46
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.46
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.46
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.46
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.46
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.46
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.46
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.46
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.46
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.46
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.46
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.46
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.46
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.46
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.46
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.46
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.46
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.46
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.46
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.46
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.46
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.46
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.46
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.46
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.46
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.46
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.46
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.46
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.46
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.46
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.46
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.46
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.46
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.46/101.46
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.46/101.46
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.46/101.46
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.46/101.46
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(s(0)) → c38(S(ok(0)), PROPER(0)) 327.46/101.46
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(s(nil)) → c38(S(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.46
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.46
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.46
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.46
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.46
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.46
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.46
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.46
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.46
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.46
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.46
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.46
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.46
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.46
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.46
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.46
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.46
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.46
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.46
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.46
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.46
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.46
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.46
S(ok(z0)) → c44(S(z0)) 327.46/101.46
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.46
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.46
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.46
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.46
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.46
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.46
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.46
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.46
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.46
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.46
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.46
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.46
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.46
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.46
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.46
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.46
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.46
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.46
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.46
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.46
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.46
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.46
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.46
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.46
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.46
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.46
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.46
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.46
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.46
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.46
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.46
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.46
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.46
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.46
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.46
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.46
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.46
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.46
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.46
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.46
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.46
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.46
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.46
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.46
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.46
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.46
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.46
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.46
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.46
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.46
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.46
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.46
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.46
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.46
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.46
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.46
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.46
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.46
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.46
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.46
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.46
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.48
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.48
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.48
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.48
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.48
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.48
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.46/101.48
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.46/101.48
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.48
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.48
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.48
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.48
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.46/101.48
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.48
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.48
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.48
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.46/101.48
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.46/101.48
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.48
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.48
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.48
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.48
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.46/101.48
PROPER(s(0)) → c38(S(ok(0)), PROPER(0)) 327.46/101.48
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.48
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.48
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.48
PROPER(s(nil)) → c38(S(ok(nil)), PROPER(nil))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c40, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37, c38

327.46/101.48

(45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

327.46/101.48

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.48
active(sqr(0)) → mark(0) 327.46/101.48
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.48
active(dbl(0)) → mark(0) 327.46/101.48
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.48
active(add(0, z0)) → mark(z0) 327.46/101.48
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.48
active(first(0, z0)) → mark(nil) 327.46/101.48
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.48
active(terms(z0)) → terms(active(z0)) 327.46/101.48
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.48
active(recip(z0)) → recip(active(z0)) 327.46/101.48
active(sqr(z0)) → sqr(active(z0)) 327.46/101.48
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.48
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.48
active(dbl(z0)) → dbl(active(z0)) 327.46/101.48
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.48
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.48
terms(mark(z0)) → mark(terms(z0)) 327.46/101.48
terms(ok(z0)) → ok(terms(z0)) 327.46/101.48
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.48
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.48
recip(mark(z0)) → mark(recip(z0)) 327.46/101.48
recip(ok(z0)) → ok(recip(z0)) 327.46/101.48
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.48
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.48
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.48
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.48
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.48
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.48
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.48
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.48
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.48
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.48
proper(terms(z0)) → terms(proper(z0)) 327.46/101.48
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.48
proper(recip(z0)) → recip(proper(z0)) 327.46/101.48
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.48
proper(s(z0)) → s(proper(z0)) 327.46/101.48
proper(0) → ok(0) 327.46/101.48
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.48
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.48
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.48
proper(nil) → ok(nil) 327.46/101.48
s(ok(z0)) → ok(s(z0)) 327.46/101.48
top(mark(z0)) → top(proper(z0)) 327.46/101.48
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.48
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.48
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.48
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.48
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.48
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.48
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.48
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.48
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.48
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.48
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.48
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.48
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.48
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.48
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.48
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.48
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.48
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.48
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.48
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.48
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.48
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.48
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.48
S(ok(z0)) → c44(S(z0)) 327.46/101.48
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.48
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.48
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.48
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.48
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.48
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.48
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.48
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.48
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.48
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.48
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.48
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.48
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.48
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.48
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.48
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.48
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.48
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.48
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.48
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.48
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.48
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.48
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.48
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.48
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.48
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.48
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.48
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.48
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.48
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.48
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.48
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.48
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.48
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.48
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.48
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.48
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.48
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.48
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.48
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.48
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.48
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.48
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.48
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.48
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.48
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.48
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.48
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.48
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.48
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.48
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.48
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.48
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.48
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.48
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.48
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.48
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.48
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.48
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.48
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.48
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.48
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.48
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.48
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.48
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.50
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.50
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.50
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.50
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.50
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.50
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.50
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.50
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.50
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.50
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.50
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.50
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.50
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.50
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.50
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.50
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.50
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.50
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.50
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.50
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.50
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.50
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.50
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.50
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.50
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.50
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.50
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.50
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.50
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.50
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.50
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.50
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.50
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.50
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.50
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.50
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.50
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.50
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.50
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.50
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.50
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.50
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.50
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.50
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.50
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.50
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.50
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.50
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.50
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.50
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.50
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.50
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.50
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.50
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.50
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.50
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.50
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.50
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.50
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.50
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.50
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.50
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.50
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.50
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.50
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.50
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.50
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.50
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.50
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.50
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.50
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.50
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.50
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.50
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.50
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.50
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.50
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.50
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.50
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.46/101.50
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.46/101.50
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.50
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.50
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.50
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.50
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.46/101.50
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.50
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.50
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.50
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.46/101.50
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.46/101.50
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.50
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.50
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.50
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.50
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.46/101.50
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.50
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.50
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.50
PROPER(s(0)) → c38(S(ok(0))) 327.46/101.50
PROPER(s(nil)) → c38(S(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.50
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.50
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.50
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.50
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.50
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.50
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.50
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.50
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.50
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.50
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.50
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.50
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.50
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.50
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.50
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.50
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.50
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.50
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.50
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.50
PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.50
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.50
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.50
S(ok(z0)) → c44(S(z0)) 327.46/101.50
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.50
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.50
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.50
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.50
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.50
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.50
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.50
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.50
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.50
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.50
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.50
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.50
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.50
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.50
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.50
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.50
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.50
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.50
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.50
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.50
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.50
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.50
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.46/101.50
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.46/101.50
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.46/101.50
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.50
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.46/101.50
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.46/101.50
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.46/101.50
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.46/101.50
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.50
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.50
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.50
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.50
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.50
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.50
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.50
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.50
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.50
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.50
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.50
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.50
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.50
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.50
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.50
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.50
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.46/101.50
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.50
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.46/101.50
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.46/101.50
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.50
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.50
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.46/101.50
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.46/101.50
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.50
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.50
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.50
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.46/101.50
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.50
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.50
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.50
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.46/101.50
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.46/101.50
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.46/101.50
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.46/101.50
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.46/101.50
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.46/101.50
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.46/101.50
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.46/101.50
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.46/101.50
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.46/101.50
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.46/101.50
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.46/101.50
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.46/101.50
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.46/101.50
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.50
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.46/101.50
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.50
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.46/101.50
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.50
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.46/101.50
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.50
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.46/101.50
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.46/101.50
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.46/101.50
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.46/101.50
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.50
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.50
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.50
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.50
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.46/101.50
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.50
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.50
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.50
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.46/101.50
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.46/101.50
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.50
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.50
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.50
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.50
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.50
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.50
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.50
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.50
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.50
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.50
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.50
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.50
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.50
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.50
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.50
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.50
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.46/101.50
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.46/101.50
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.46/101.50
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.46/101.50
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.50
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.50
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.50
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.50
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.46/101.50
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.50
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.50
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.50
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.46/101.50
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.46/101.50
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.50
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.50
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.50
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.50
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.46/101.50
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.50
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.50
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.50
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.46/101.50
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.46/101.50
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.46/101.50
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.46/101.50
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.46/101.50
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.46/101.50
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.46/101.50
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.46/101.50
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.46/101.50
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.46/101.50
PROPER(s(0)) → c38(S(ok(0))) 327.46/101.50
PROPER(s(nil)) → c38(S(ok(nil)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c40, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37, c38, c38

327.46/101.50

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(add(z0, z1)) → c40(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.46/101.50
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.46/101.50
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.46/101.50
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.46/101.50
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.46/101.50
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 327.46/101.50
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.46/101.50
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.46/101.50
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.46/101.50
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 327.46/101.50
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.46/101.50
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.46/101.50
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.46/101.50
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.46/101.50
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.46/101.50
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 327.46/101.50
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.46/101.50
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.46/101.50
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.46/101.50
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

327.46/101.50

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.46/101.50
active(sqr(0)) → mark(0) 327.46/101.50
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.46/101.50
active(dbl(0)) → mark(0) 327.46/101.50
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.46/101.50
active(add(0, z0)) → mark(z0) 327.46/101.50
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.46/101.50
active(first(0, z0)) → mark(nil) 327.46/101.50
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.46/101.50
active(terms(z0)) → terms(active(z0)) 327.46/101.50
active(cons(z0, z1)) → cons(active(z0), z1) 327.46/101.50
active(recip(z0)) → recip(active(z0)) 327.46/101.50
active(sqr(z0)) → sqr(active(z0)) 327.46/101.50
active(add(z0, z1)) → add(active(z0), z1) 327.46/101.50
active(add(z0, z1)) → add(z0, active(z1)) 327.46/101.50
active(dbl(z0)) → dbl(active(z0)) 327.46/101.50
active(first(z0, z1)) → first(active(z0), z1) 327.46/101.50
active(first(z0, z1)) → first(z0, active(z1)) 327.46/101.50
terms(mark(z0)) → mark(terms(z0)) 327.46/101.50
terms(ok(z0)) → ok(terms(z0)) 327.46/101.50
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.46/101.50
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.46/101.50
recip(mark(z0)) → mark(recip(z0)) 327.46/101.50
recip(ok(z0)) → ok(recip(z0)) 327.46/101.50
sqr(mark(z0)) → mark(sqr(z0)) 327.46/101.50
sqr(ok(z0)) → ok(sqr(z0)) 327.46/101.50
add(mark(z0), z1) → mark(add(z0, z1)) 327.46/101.50
add(z0, mark(z1)) → mark(add(z0, z1)) 327.46/101.50
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.46/101.50
dbl(mark(z0)) → mark(dbl(z0)) 327.46/101.50
dbl(ok(z0)) → ok(dbl(z0)) 327.46/101.50
first(mark(z0), z1) → mark(first(z0, z1)) 327.46/101.50
first(z0, mark(z1)) → mark(first(z0, z1)) 327.46/101.50
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.46/101.50
proper(terms(z0)) → terms(proper(z0)) 327.46/101.50
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.46/101.50
proper(recip(z0)) → recip(proper(z0)) 327.46/101.50
proper(sqr(z0)) → sqr(proper(z0)) 327.46/101.50
proper(s(z0)) → s(proper(z0)) 327.46/101.50
proper(0) → ok(0) 327.46/101.50
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.46/101.50
proper(dbl(z0)) → dbl(proper(z0)) 327.46/101.50
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.46/101.50
proper(nil) → ok(nil) 327.46/101.50
s(ok(z0)) → ok(s(z0)) 327.46/101.50
top(mark(z0)) → top(proper(z0)) 327.46/101.50
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.46/101.50
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.46/101.50
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.46/101.50
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.46/101.50
TERMS(mark(z0)) → c18(TERMS(z0)) 327.46/101.50
TERMS(ok(z0)) → c19(TERMS(z0)) 327.46/101.50
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.46/101.50
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.46/101.50
RECIP(mark(z0)) → c22(RECIP(z0)) 327.46/101.50
RECIP(ok(z0)) → c23(RECIP(z0)) 327.46/101.50
SQR(mark(z0)) → c24(SQR(z0)) 327.46/101.50
SQR(ok(z0)) → c25(SQR(z0)) 327.46/101.50
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.46/101.50
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.46/101.50
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.46/101.50
DBL(mark(z0)) → c29(DBL(z0)) 327.46/101.50
DBL(ok(z0)) → c30(DBL(z0)) 327.46/101.50
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.46/101.50
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.46/101.50
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.46/101.50
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.46/101.50
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.46/101.50
S(ok(z0)) → c44(S(z0)) 327.46/101.50
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.46/101.50
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.46/101.50
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.46/101.50
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.46/101.50
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.46/101.50
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.46/101.50
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.46/101.50
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.46/101.50
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.46/101.50
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.46/101.50
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.46/101.50
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.46/101.50
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.46/101.50
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.46/101.50
ACTIVE(terms(z0)) → c1(S(z0)) 327.46/101.50
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.46/101.50
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.46/101.50
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.46/101.50
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.46/101.50
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.50
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.50
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.50
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.50
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.50
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.50
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.50
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.50
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.50
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.50
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.50
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.50
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.50
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.50
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.50
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.50
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.50
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.50
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.50
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.50
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.50
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.50
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.50
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.50
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.50
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.50
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.50
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.50
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.50
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.50
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.50
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.50
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.50
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.50
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.50
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.50
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.50
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.50
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.50
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.50
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.50
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.50
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.50
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.50
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.50
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.50
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.50
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.50
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.50
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.50
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.50
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.50
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.50
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.50
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.50
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.50
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.50
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.50
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.50
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.50
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.50
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.50
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.50
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.50
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.50
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.50
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.50
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.50
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.50
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.50
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.50
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.50
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.50
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.50
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.50
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.50
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.50
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.50
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.50
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.50
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.50
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.50
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.50
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.50
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.50
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.50
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.50
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.50
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.50
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.50
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.50
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.50
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.50
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.50
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.50
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.50
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.50
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.50
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.50
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.50
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.50
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.50
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.50
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.50
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.50
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.50
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.50
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.50
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.50
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.50
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.50
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.50
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.50
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.50
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.50
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.50
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.50
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.50
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.50
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.50
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.50
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.50
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.50
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.50
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.50
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.50
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.50
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.50
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.50
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.50
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.50
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.50
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.50
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.50
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.50
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.50
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.50
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.50
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.50
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.50
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.50
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.50
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.50
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.50
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.50
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.50
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.50
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.50
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.50
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.50
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.50
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.51
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.51
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.51
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.51
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.51
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.51
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 327.83/101.51
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.51
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.51
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.51
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 327.83/101.51
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 327.83/101.51
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.51
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.51
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.51
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.51
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.51
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.51
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.51
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.51
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.51
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.51
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.51
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.51
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.51
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.51
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.51
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.51
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.83/101.51
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.83/101.51
S(ok(z0)) → c44(S(z0)) 327.83/101.51
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.51
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.51
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.51
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.51
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.51
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.51
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.51
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.51
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.51
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.51
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.51
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.51
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.51
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.51
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.51
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.51
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.51
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.51
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.51
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.51
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.51
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.51
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.51
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.51
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.51
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.51
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.51
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.51
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.51
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.51
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.51
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.51
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.51
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.51
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.51
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 327.83/101.51
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.51
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.51
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.51
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 327.83/101.51
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 327.83/101.51
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37, c38, c38, c40

327.83/101.51

(49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 4 trailing tuple parts

327.83/101.51

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.51
active(sqr(0)) → mark(0) 327.83/101.51
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.51
active(dbl(0)) → mark(0) 327.83/101.51
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.51
active(add(0, z0)) → mark(z0) 327.83/101.51
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.51
active(first(0, z0)) → mark(nil) 327.83/101.51
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.51
active(terms(z0)) → terms(active(z0)) 327.83/101.51
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.51
active(recip(z0)) → recip(active(z0)) 327.83/101.51
active(sqr(z0)) → sqr(active(z0)) 327.83/101.51
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.51
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.51
active(dbl(z0)) → dbl(active(z0)) 327.83/101.51
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.51
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.51
terms(mark(z0)) → mark(terms(z0)) 327.83/101.51
terms(ok(z0)) → ok(terms(z0)) 327.83/101.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.51
recip(mark(z0)) → mark(recip(z0)) 327.83/101.51
recip(ok(z0)) → ok(recip(z0)) 327.83/101.51
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.51
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.51
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.51
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.51
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.51
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.51
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.51
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.51
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.51
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.51
proper(terms(z0)) → terms(proper(z0)) 327.83/101.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.51
proper(recip(z0)) → recip(proper(z0)) 327.83/101.51
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.51
proper(s(z0)) → s(proper(z0)) 327.83/101.51
proper(0) → ok(0) 327.83/101.51
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.51
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.51
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.51
proper(nil) → ok(nil) 327.83/101.51
s(ok(z0)) → ok(s(z0)) 327.83/101.51
top(mark(z0)) → top(proper(z0)) 327.83/101.51
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.51
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.51
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.51
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.51
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.51
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.51
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.51
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.51
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.51
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.51
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.51
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.51
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.51
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.51
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.51
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.51
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.83/101.51
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.83/101.51
S(ok(z0)) → c44(S(z0)) 327.83/101.51
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.83/101.51
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.51
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.51
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.51
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.51
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.51
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.51
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.51
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.51
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.51
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.51
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.51
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.51
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.51
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.51
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.51
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.51
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.51
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.51
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.51
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.51
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.51
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.51
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.51
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.51
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.51
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.51
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.51
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.51
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.51
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.51
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.51
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.51
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.51
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.51
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.51
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.51
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.51
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.51
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.51
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.51
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.51
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.51
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.51
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.51
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.51
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.51
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.51
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.51
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.51
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.51
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.51
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.51
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.51
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.51
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.51
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.51
PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) 327.83/101.51
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.83/101.51
S(ok(z0)) → c44(S(z0)) 327.83/101.51
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.51
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.51
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.51
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.51
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.51
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.51
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.51
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.51
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.51
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.51
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.51
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.51
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.51
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.51
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.51
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.51
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.51
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.51
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.51
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.51
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.51
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.51
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.51
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.51
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.51
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.51
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.51
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.51
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.51
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.51
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.51
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.51
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.51
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.51
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.51
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.51
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.51
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.51
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.51
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.51
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c41, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37, c38, c38, c40, c40

327.83/101.51

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(dbl(z0)) → c41(DBL(proper(z0)), PROPER(z0)) by

PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(dbl(0)) → c41(DBL(ok(0)), PROPER(0)) 327.83/101.51
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(dbl(nil)) → c41(DBL(ok(nil)), PROPER(nil))

327.83/101.51

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.51
active(sqr(0)) → mark(0) 327.83/101.51
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.51
active(dbl(0)) → mark(0) 327.83/101.51
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.51
active(add(0, z0)) → mark(z0) 327.83/101.51
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.51
active(first(0, z0)) → mark(nil) 327.83/101.51
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.51
active(terms(z0)) → terms(active(z0)) 327.83/101.51
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.51
active(recip(z0)) → recip(active(z0)) 327.83/101.51
active(sqr(z0)) → sqr(active(z0)) 327.83/101.51
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.51
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.51
active(dbl(z0)) → dbl(active(z0)) 327.83/101.51
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.51
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.51
terms(mark(z0)) → mark(terms(z0)) 327.83/101.51
terms(ok(z0)) → ok(terms(z0)) 327.83/101.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.51
recip(mark(z0)) → mark(recip(z0)) 327.83/101.51
recip(ok(z0)) → ok(recip(z0)) 327.83/101.51
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.51
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.51
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.51
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.51
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.51
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.51
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.51
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.51
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.51
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.51
proper(terms(z0)) → terms(proper(z0)) 327.83/101.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.51
proper(recip(z0)) → recip(proper(z0)) 327.83/101.51
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.51
proper(s(z0)) → s(proper(z0)) 327.83/101.51
proper(0) → ok(0) 327.83/101.51
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.51
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.51
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.51
proper(nil) → ok(nil) 327.83/101.51
s(ok(z0)) → ok(s(z0)) 327.83/101.51
top(mark(z0)) → top(proper(z0)) 327.83/101.51
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.51
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.51
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.51
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.51
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.51
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.51
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.51
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.51
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.51
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.51
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.51
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.51
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.51
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.51
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.51
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.51
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.83/101.51
S(ok(z0)) → c44(S(z0)) 327.83/101.51
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.83/101.51
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.51
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.51
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.51
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.51
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.51
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.51
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.51
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.51
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.51
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.51
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.51
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.51
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.51
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.51
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.51
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.51
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.51
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.51
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.51
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.51
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.51
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.51
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.51
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.51
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.51
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.51
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.51
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.51
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.51
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.51
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.51
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.51
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.51
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.51
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.51
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.51
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.51
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.51
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.51
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.51
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(dbl(0)) → c41(DBL(ok(0)), PROPER(0)) 327.83/101.51
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(dbl(nil)) → c41(DBL(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.51
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.51
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.51
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.51
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.51
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.51
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.51
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.51
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.51
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.51
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.51
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.51
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.51
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.51
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.51
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.51
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.83/101.51
S(ok(z0)) → c44(S(z0)) 327.83/101.51
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.51
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.51
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.51
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.51
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.51
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.51
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.51
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.51
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.51
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.51
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.51
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.51
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.51
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.51
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.51
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.51
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.51
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.51
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.51
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.51
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.51
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.51
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.51
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.51
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.51
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.51
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.51
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.51
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.51
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.51
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.51
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.51
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.51
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.51
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.51
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.51
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.51
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.51
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.51
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.51
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.51
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.51
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.51
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.51
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.51
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.51
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.51
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.51
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.51
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.51
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.51
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.51
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.51
PROPER(dbl(0)) → c41(DBL(ok(0)), PROPER(0)) 327.83/101.51
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.51
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.51
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.51
PROPER(dbl(nil)) → c41(DBL(ok(nil)), PROPER(nil))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37, c38, c38, c40, c40, c41

327.83/101.51

(53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

327.83/101.51

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.51
active(sqr(0)) → mark(0) 327.83/101.51
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.51
active(dbl(0)) → mark(0) 327.83/101.51
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.51
active(add(0, z0)) → mark(z0) 327.83/101.51
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.51
active(first(0, z0)) → mark(nil) 327.83/101.51
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.51
active(terms(z0)) → terms(active(z0)) 327.83/101.51
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.51
active(recip(z0)) → recip(active(z0)) 327.83/101.51
active(sqr(z0)) → sqr(active(z0)) 327.83/101.51
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.51
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.51
active(dbl(z0)) → dbl(active(z0)) 327.83/101.51
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.51
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.51
terms(mark(z0)) → mark(terms(z0)) 327.83/101.51
terms(ok(z0)) → ok(terms(z0)) 327.83/101.51
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.51
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.51
recip(mark(z0)) → mark(recip(z0)) 327.83/101.51
recip(ok(z0)) → ok(recip(z0)) 327.83/101.51
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.51
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.51
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.51
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.51
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.51
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.51
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.51
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.51
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.51
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.51
proper(terms(z0)) → terms(proper(z0)) 327.83/101.51
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.51
proper(recip(z0)) → recip(proper(z0)) 327.83/101.51
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.51
proper(s(z0)) → s(proper(z0)) 327.83/101.51
proper(0) → ok(0) 327.83/101.51
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.51
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.51
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.51
proper(nil) → ok(nil) 327.83/101.51
s(ok(z0)) → ok(s(z0)) 327.83/101.51
top(mark(z0)) → top(proper(z0)) 327.83/101.51
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.51
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.51
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.51
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.51
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.51
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.51
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.51
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.51
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.51
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.51
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.51
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.51
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.51
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.51
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.51
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.51
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.51
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.51
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.83/101.51
S(ok(z0)) → c44(S(z0)) 327.83/101.51
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.83/101.51
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.51
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.51
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.51
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.51
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.51
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.51
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.51
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.51
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.51
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.51
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.51
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.51
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.51
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.51
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.52
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.52
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.52
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.52
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.52
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.52
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.52
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.52
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.52
PROPER(dbl(nil)) → c41(DBL(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.52
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.52
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.52
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.52
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.52
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.52
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.52
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.52
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.52
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.52
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.52
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.52
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.52
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.52
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.52
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.52
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.52
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.52
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.52
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.52
PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 327.83/101.52
S(ok(z0)) → c44(S(z0)) 327.83/101.52
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.52
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.52
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.52
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.52
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.52
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.52
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.52
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.52
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.52
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.52
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.52
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.52
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.52
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.52
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.52
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.52
PROPER(dbl(nil)) → c41(DBL(ok(nil)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, PROPER, S, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c42, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37, c38, c38, c40, c40, c41, c41

327.83/101.52

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace PROPER(first(z0, z1)) → c42(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 327.83/101.52
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 327.83/101.52
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 327.83/101.52
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

327.83/101.52

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.52
active(sqr(0)) → mark(0) 327.83/101.52
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.52
active(dbl(0)) → mark(0) 327.83/101.52
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.52
active(add(0, z0)) → mark(z0) 327.83/101.52
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.52
active(first(0, z0)) → mark(nil) 327.83/101.52
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.52
active(terms(z0)) → terms(active(z0)) 327.83/101.52
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.52
active(recip(z0)) → recip(active(z0)) 327.83/101.52
active(sqr(z0)) → sqr(active(z0)) 327.83/101.52
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.52
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.52
active(dbl(z0)) → dbl(active(z0)) 327.83/101.52
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.52
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.52
terms(mark(z0)) → mark(terms(z0)) 327.83/101.52
terms(ok(z0)) → ok(terms(z0)) 327.83/101.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.52
recip(mark(z0)) → mark(recip(z0)) 327.83/101.52
recip(ok(z0)) → ok(recip(z0)) 327.83/101.52
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.52
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.52
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.52
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.52
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.52
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.52
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.52
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.52
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.52
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.52
proper(terms(z0)) → terms(proper(z0)) 327.83/101.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.52
proper(recip(z0)) → recip(proper(z0)) 327.83/101.52
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.52
proper(s(z0)) → s(proper(z0)) 327.83/101.52
proper(0) → ok(0) 327.83/101.52
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.52
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.52
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.52
proper(nil) → ok(nil) 327.83/101.52
s(ok(z0)) → ok(s(z0)) 327.83/101.52
top(mark(z0)) → top(proper(z0)) 327.83/101.52
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.52
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.52
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.52
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.52
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.52
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.52
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.52
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.52
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.52
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.52
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.52
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.52
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.52
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.52
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.52
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.52
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.52
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.52
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.52
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.52
S(ok(z0)) → c44(S(z0)) 327.83/101.52
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.83/101.52
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.52
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.52
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.52
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.52
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.52
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.52
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.52
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.52
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.52
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.52
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.52
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.52
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.52
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.52
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.52
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.52
PROPER(dbl(nil)) → c41(DBL(ok(nil))) 327.83/101.52
PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 327.83/101.52
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 327.83/101.52
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 327.83/101.52
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.52
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.52
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.52
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.52
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.52
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.52
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.52
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.52
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.52
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.52
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.52
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.52
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.52
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.52
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.52
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.52
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.52
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.52
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.52
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.52
S(ok(z0)) → c44(S(z0)) 327.83/101.52
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.52
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.52
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.52
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.52
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.52
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.52
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.52
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.52
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.52
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.52
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.52
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.52
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.52
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.52
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.52
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.52
PROPER(dbl(nil)) → c41(DBL(ok(nil))) 327.83/101.52
PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 327.83/101.52
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 327.83/101.52
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 327.83/101.52
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S, TOP, PROPER

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37, c38, c38, c40, c40, c41, c41, c42

327.83/101.52

(57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 4 trailing tuple parts

327.83/101.52

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.52
active(sqr(0)) → mark(0) 327.83/101.52
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.52
active(dbl(0)) → mark(0) 327.83/101.52
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.52
active(add(0, z0)) → mark(z0) 327.83/101.52
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.52
active(first(0, z0)) → mark(nil) 327.83/101.52
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.52
active(terms(z0)) → terms(active(z0)) 327.83/101.52
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.52
active(recip(z0)) → recip(active(z0)) 327.83/101.52
active(sqr(z0)) → sqr(active(z0)) 327.83/101.52
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.52
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.52
active(dbl(z0)) → dbl(active(z0)) 327.83/101.52
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.52
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.52
terms(mark(z0)) → mark(terms(z0)) 327.83/101.52
terms(ok(z0)) → ok(terms(z0)) 327.83/101.52
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.52
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.52
recip(mark(z0)) → mark(recip(z0)) 327.83/101.52
recip(ok(z0)) → ok(recip(z0)) 327.83/101.52
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.52
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.52
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.52
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.52
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.52
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.52
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.52
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.52
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.52
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.52
proper(terms(z0)) → terms(proper(z0)) 327.83/101.52
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.52
proper(recip(z0)) → recip(proper(z0)) 327.83/101.52
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.52
proper(s(z0)) → s(proper(z0)) 327.83/101.52
proper(0) → ok(0) 327.83/101.52
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.52
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.52
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.52
proper(nil) → ok(nil) 327.83/101.52
s(ok(z0)) → ok(s(z0)) 327.83/101.52
top(mark(z0)) → top(proper(z0)) 327.83/101.52
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.52
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.52
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.52
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.52
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.52
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.52
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.52
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.52
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.52
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.52
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.52
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.52
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.52
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.52
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.52
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.52
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.52
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.52
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.52
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.52
S(ok(z0)) → c44(S(z0)) 327.83/101.52
TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) 327.83/101.52
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.52
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.52
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.52
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.52
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.52
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.52
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.52
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.52
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.52
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.52
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.52
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.52
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.52
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.52
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.52
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.52
PROPER(dbl(nil)) → c41(DBL(ok(nil))) 327.83/101.52
PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.52
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.52
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.52
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.52
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.52
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.52
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.52
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.52
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.52
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.52
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.52
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.52
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.52
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.52
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.52
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.52
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.52
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.52
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.52
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.52
S(ok(z0)) → c44(S(z0)) 327.83/101.52
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.52
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.52
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.52
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.52
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.52
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.52
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.52
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.52
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.52
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.52
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.52
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.52
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.52
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.52
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.52
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.52
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.52
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.52
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.52
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.52
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.52
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.52
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.52
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.52
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.52
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.52
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.52
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.52
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.52
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.52
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.52
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.52
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.52
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.52
PROPER(dbl(nil)) → c41(DBL(ok(nil))) 327.83/101.52
PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.52
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.52
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.52
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.52
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.52
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.52
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.52
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.52
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.52
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.52
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0)) 327.83/101.52
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.52
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(x1)) 327.83/101.52
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S, TOP, PROPER

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44, c45, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37, c38, c38, c40, c40, c41, c41, c42, c42

327.83/101.52

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(terms(z0))) → c45(TOP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.52
TOP(mark(cons(z0, z1))) → c45(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.52
TOP(mark(recip(z0))) → c45(TOP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.52
TOP(mark(sqr(z0))) → c45(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.52
TOP(mark(s(z0))) → c45(TOP(s(proper(z0))), PROPER(s(z0))) 327.83/101.52
TOP(mark(0)) → c45(TOP(ok(0)), PROPER(0)) 327.83/101.52
TOP(mark(add(z0, z1))) → c45(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.52
TOP(mark(dbl(z0))) → c45(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.52
TOP(mark(first(z0, z1))) → c45(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.52
TOP(mark(nil)) → c45(TOP(ok(nil)), PROPER(nil))

327.83/101.52

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.52
active(sqr(0)) → mark(0) 327.83/101.52
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.52
active(dbl(0)) → mark(0) 327.83/101.52
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.52
active(add(0, z0)) → mark(z0) 327.83/101.52
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.52
active(first(0, z0)) → mark(nil) 327.83/101.52
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.53
active(terms(z0)) → terms(active(z0)) 327.83/101.53
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.53
active(recip(z0)) → recip(active(z0)) 327.83/101.53
active(sqr(z0)) → sqr(active(z0)) 327.83/101.53
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.53
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.53
active(dbl(z0)) → dbl(active(z0)) 327.83/101.53
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.53
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.53
terms(mark(z0)) → mark(terms(z0)) 327.83/101.53
terms(ok(z0)) → ok(terms(z0)) 327.83/101.53
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.53
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.53
recip(mark(z0)) → mark(recip(z0)) 327.83/101.53
recip(ok(z0)) → ok(recip(z0)) 327.83/101.53
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.53
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.53
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.53
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.53
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.53
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.53
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.53
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.53
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.53
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.53
proper(terms(z0)) → terms(proper(z0)) 327.83/101.53
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.53
proper(recip(z0)) → recip(proper(z0)) 327.83/101.53
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.53
proper(s(z0)) → s(proper(z0)) 327.83/101.53
proper(0) → ok(0) 327.83/101.53
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.53
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.53
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.53
proper(nil) → ok(nil) 327.83/101.53
s(ok(z0)) → ok(s(z0)) 327.83/101.53
top(mark(z0)) → top(proper(z0)) 327.83/101.53
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.53
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.53
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.53
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.53
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.53
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.53
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.53
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.53
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.53
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.53
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.53
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.53
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.53
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.53
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.53
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.53
S(ok(z0)) → c44(S(z0)) 327.83/101.53
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.53
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.53
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.53
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.53
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.53
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.53
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.53
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.53
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.53
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.53
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.53
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.53
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.53
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.53
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.53
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.53
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.53
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.53
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.53
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.53
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.53
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.53
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.53
PROPER(dbl(nil)) → c41(DBL(ok(nil))) 327.83/101.53
PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
TOP(mark(terms(z0))) → c45(TOP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
TOP(mark(cons(z0, z1))) → c45(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
TOP(mark(recip(z0))) → c45(TOP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
TOP(mark(sqr(z0))) → c45(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
TOP(mark(s(z0))) → c45(TOP(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
TOP(mark(0)) → c45(TOP(ok(0)), PROPER(0)) 327.83/101.53
TOP(mark(add(z0, z1))) → c45(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
TOP(mark(dbl(z0))) → c45(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
TOP(mark(first(z0, z1))) → c45(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
TOP(mark(nil)) → c45(TOP(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.53
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.53
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.53
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.53
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.53
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.53
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.53
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.53
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.53
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.53
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.53
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.53
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.53
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.53
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.53
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.53
S(ok(z0)) → c44(S(z0)) 327.83/101.53
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.53
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.53
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.53
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.53
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.53
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.53
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.53
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.53
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.53
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.53
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.53
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.53
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.53
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.53
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.53
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.53
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.53
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.53
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.53
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.53
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.53
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.53
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.53
PROPER(dbl(nil)) → c41(DBL(ok(nil))) 327.83/101.53
PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S, TOP, PROPER

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37, c38, c38, c40, c40, c41, c41, c42, c42, c45

327.83/101.53

(61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

327.83/101.53

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.53
active(sqr(0)) → mark(0) 327.83/101.53
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.53
active(dbl(0)) → mark(0) 327.83/101.53
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.53
active(add(0, z0)) → mark(z0) 327.83/101.53
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.53
active(first(0, z0)) → mark(nil) 327.83/101.53
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.53
active(terms(z0)) → terms(active(z0)) 327.83/101.53
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.53
active(recip(z0)) → recip(active(z0)) 327.83/101.53
active(sqr(z0)) → sqr(active(z0)) 327.83/101.53
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.53
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.53
active(dbl(z0)) → dbl(active(z0)) 327.83/101.53
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.53
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.53
terms(mark(z0)) → mark(terms(z0)) 327.83/101.53
terms(ok(z0)) → ok(terms(z0)) 327.83/101.53
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.53
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.53
recip(mark(z0)) → mark(recip(z0)) 327.83/101.53
recip(ok(z0)) → ok(recip(z0)) 327.83/101.53
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.53
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.53
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.53
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.53
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.53
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.53
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.53
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.53
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.53
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.53
proper(terms(z0)) → terms(proper(z0)) 327.83/101.53
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.53
proper(recip(z0)) → recip(proper(z0)) 327.83/101.53
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.53
proper(s(z0)) → s(proper(z0)) 327.83/101.53
proper(0) → ok(0) 327.83/101.53
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.53
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.53
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.53
proper(nil) → ok(nil) 327.83/101.53
s(ok(z0)) → ok(s(z0)) 327.83/101.53
top(mark(z0)) → top(proper(z0)) 327.83/101.53
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.53
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.53
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.53
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.53
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.53
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.53
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.53
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.53
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.53
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.53
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.53
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.53
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.53
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.53
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.53
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.53
S(ok(z0)) → c44(S(z0)) 327.83/101.53
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.53
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.53
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.53
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.53
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.53
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.53
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.53
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.53
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.53
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.53
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.53
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.53
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.53
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.53
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.53
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.53
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.53
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.53
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.53
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.53
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.53
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.53
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.53
PROPER(dbl(nil)) → c41(DBL(ok(nil))) 327.83/101.53
PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
TOP(mark(terms(z0))) → c45(TOP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
TOP(mark(cons(z0, z1))) → c45(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
TOP(mark(recip(z0))) → c45(TOP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
TOP(mark(sqr(z0))) → c45(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
TOP(mark(s(z0))) → c45(TOP(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
TOP(mark(add(z0, z1))) → c45(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
TOP(mark(dbl(z0))) → c45(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
TOP(mark(first(z0, z1))) → c45(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
TOP(mark(0)) → c45(TOP(ok(0))) 327.83/101.53
TOP(mark(nil)) → c45(TOP(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.53
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.53
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.53
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.53
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.53
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.53
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.53
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.53
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.53
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.53
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.53
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.53
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.53
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.53
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.53
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.53
S(ok(z0)) → c44(S(z0)) 327.83/101.53
TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.53
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.53
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.53
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.53
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.53
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.53
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.53
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.53
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.53
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.53
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.53
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.53
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.53
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.53
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.53
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.53
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.53
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.53
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.53
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.53
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.53
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.53
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.53
PROPER(dbl(nil)) → c41(DBL(ok(nil))) 327.83/101.53
PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(x1))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S, TOP, PROPER

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44, c46, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37, c38, c38, c40, c40, c41, c41, c42, c42, c45, c45

327.83/101.53

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID) transformation)

Use narrowing to replace TOP(ok(z0)) → c46(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(terms(z0))) → c46(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
TOP(ok(sqr(0))) → c46(TOP(mark(0)), ACTIVE(sqr(0))) 327.83/101.53
TOP(ok(sqr(s(z0)))) → c46(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.83/101.53
TOP(ok(dbl(0))) → c46(TOP(mark(0)), ACTIVE(dbl(0))) 327.83/101.53
TOP(ok(dbl(s(z0)))) → c46(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.83/101.53
TOP(ok(add(0, z0))) → c46(TOP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
TOP(ok(add(s(z0), z1))) → c46(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
TOP(ok(first(0, z0))) → c46(TOP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
TOP(ok(first(s(z0), cons(z1, z2)))) → c46(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
TOP(ok(terms(z0))) → c46(TOP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
TOP(ok(cons(z0, z1))) → c46(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
TOP(ok(recip(z0))) → c46(TOP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
TOP(ok(sqr(z0))) → c46(TOP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
TOP(ok(add(z0, z1))) → c46(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
TOP(ok(add(z0, z1))) → c46(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
TOP(ok(dbl(z0))) → c46(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
TOP(ok(first(z0, z1))) → c46(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
TOP(ok(first(z0, z1))) → c46(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

327.83/101.53

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.53
active(sqr(0)) → mark(0) 327.83/101.53
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.53
active(dbl(0)) → mark(0) 327.83/101.53
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.53
active(add(0, z0)) → mark(z0) 327.83/101.53
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.53
active(first(0, z0)) → mark(nil) 327.83/101.53
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.53
active(terms(z0)) → terms(active(z0)) 327.83/101.53
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.53
active(recip(z0)) → recip(active(z0)) 327.83/101.53
active(sqr(z0)) → sqr(active(z0)) 327.83/101.53
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.53
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.53
active(dbl(z0)) → dbl(active(z0)) 327.83/101.53
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.53
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.53
terms(mark(z0)) → mark(terms(z0)) 327.83/101.53
terms(ok(z0)) → ok(terms(z0)) 327.83/101.53
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.53
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.53
recip(mark(z0)) → mark(recip(z0)) 327.83/101.53
recip(ok(z0)) → ok(recip(z0)) 327.83/101.53
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.53
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.53
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.53
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.53
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.53
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.53
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.53
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.53
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.53
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.53
proper(terms(z0)) → terms(proper(z0)) 327.83/101.53
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.53
proper(recip(z0)) → recip(proper(z0)) 327.83/101.53
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.53
proper(s(z0)) → s(proper(z0)) 327.83/101.53
proper(0) → ok(0) 327.83/101.53
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.53
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.53
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.53
proper(nil) → ok(nil) 327.83/101.53
s(ok(z0)) → ok(s(z0)) 327.83/101.53
top(mark(z0)) → top(proper(z0)) 327.83/101.53
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.53
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.53
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.53
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.53
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.53
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.53
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.53
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.53
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.53
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.53
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.53
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.53
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.53
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.53
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.53
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.53
S(ok(z0)) → c44(S(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.53
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.53
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.53
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.53
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.53
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.53
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.53
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.53
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.53
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.53
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.53
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.53
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.53
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.53
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.53
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.53
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.53
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.53
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.53
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.53
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.53
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.53
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.53
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.53
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.53
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.53
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.53
PROPER(dbl(nil)) → c41(DBL(ok(nil))) 327.83/101.53
PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.53
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.53
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.53
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.53
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.53
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.53
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.53
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.53
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.53
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.53
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0)) 327.83/101.53
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.53
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(x1)) 327.83/101.53
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.53
TOP(mark(terms(z0))) → c45(TOP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.53
TOP(mark(cons(z0, z1))) → c45(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.53
TOP(mark(recip(z0))) → c45(TOP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.53
TOP(mark(sqr(z0))) → c45(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.53
TOP(mark(s(z0))) → c45(TOP(s(proper(z0))), PROPER(s(z0))) 327.83/101.53
TOP(mark(add(z0, z1))) → c45(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.53
TOP(mark(dbl(z0))) → c45(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.53
TOP(mark(first(z0, z1))) → c45(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.53
TOP(mark(0)) → c45(TOP(ok(0))) 327.83/101.53
TOP(mark(nil)) → c45(TOP(ok(nil))) 327.83/101.53
TOP(ok(terms(z0))) → c46(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
TOP(ok(sqr(0))) → c46(TOP(mark(0)), ACTIVE(sqr(0))) 327.83/101.53
TOP(ok(sqr(s(z0)))) → c46(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.83/101.53
TOP(ok(dbl(0))) → c46(TOP(mark(0)), ACTIVE(dbl(0))) 327.83/101.53
TOP(ok(dbl(s(z0)))) → c46(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.83/101.53
TOP(ok(add(0, z0))) → c46(TOP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
TOP(ok(add(s(z0), z1))) → c46(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
TOP(ok(first(0, z0))) → c46(TOP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
TOP(ok(first(s(z0), cons(z1, z2)))) → c46(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
TOP(ok(terms(z0))) → c46(TOP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
TOP(ok(cons(z0, z1))) → c46(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
TOP(ok(recip(z0))) → c46(TOP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
TOP(ok(sqr(z0))) → c46(TOP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
TOP(ok(add(z0, z1))) → c46(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
TOP(ok(add(z0, z1))) → c46(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
TOP(ok(dbl(z0))) → c46(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
TOP(ok(first(z0, z1))) → c46(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
TOP(ok(first(z0, z1))) → c46(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

S tuples:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.53
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.53
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.53
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.53
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.53
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.53
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.53
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.53
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.53
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.53
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.53
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.53
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.53
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.53
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.53
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.53
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.53
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.53
S(ok(z0)) → c44(S(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.53
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.53
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.53
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.53
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.53
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.53
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.53
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.53
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.53
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.53
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.53
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.53
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.53
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.53
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.53
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.54
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.54
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.54
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.54
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.54
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.54
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.54
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.54
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.54
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.54
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.54
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.54
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.54
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.54
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.54
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.54
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.54
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.54
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.54
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.54
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.54
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.54
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.54
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.54
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.54
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.54
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.54
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.54
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.54
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.54
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.54
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.54
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.54
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.54
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.54
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.54
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.54
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.54
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.54
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.54
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.54
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.54
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.54
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.54
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.54
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.54
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.54
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.54
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.54
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.54
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.54
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.54
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.54
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.54
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.54
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.54
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.54
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.54
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.54
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.54
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.54
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.54
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.54
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.54
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.54
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.54
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.54
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.54
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.54
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.54
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.54
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.54
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.54
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.54
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.54
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.54
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.54
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.54
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.54
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.54
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.54
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.54
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.54
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.54
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.54
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.54
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.54
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.54
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.54
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.54
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.54
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.54
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.54
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.54
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.54
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.54
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.54
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.54
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.54
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.54
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.54
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.54
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.54
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.54
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.54
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.54
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.54
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.54
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.54
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.54
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.54
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.54
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.54
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.54
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.54
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.54
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.54
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.54
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.54
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.54
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.54
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.54
PROPER(dbl(nil)) → c41(DBL(ok(nil))) 327.83/101.54
PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.54
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.54
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.54
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.54
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.54
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.54
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.54
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.54
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.54
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.54
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.54
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.54
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0)) 327.83/101.54
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.54
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(x1)) 327.83/101.54
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.54
TOP(ok(terms(z0))) → c46(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.54
TOP(ok(sqr(0))) → c46(TOP(mark(0)), ACTIVE(sqr(0))) 327.83/101.54
TOP(ok(sqr(s(z0)))) → c46(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.83/101.54
TOP(ok(dbl(0))) → c46(TOP(mark(0)), ACTIVE(dbl(0))) 327.83/101.54
TOP(ok(dbl(s(z0)))) → c46(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.83/101.54
TOP(ok(add(0, z0))) → c46(TOP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.54
TOP(ok(add(s(z0), z1))) → c46(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.54
TOP(ok(first(0, z0))) → c46(TOP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.54
TOP(ok(first(s(z0), cons(z1, z2)))) → c46(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.54
TOP(ok(terms(z0))) → c46(TOP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.54
TOP(ok(cons(z0, z1))) → c46(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.54
TOP(ok(recip(z0))) → c46(TOP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.54
TOP(ok(sqr(z0))) → c46(TOP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.54
TOP(ok(add(z0, z1))) → c46(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.54
TOP(ok(add(z0, z1))) → c46(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.54
TOP(ok(dbl(z0))) → c46(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.54
TOP(ok(first(z0, z1))) → c46(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.54
TOP(ok(first(z0, z1))) → c46(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

K tuples:

TOP(mark(z0)) → c45(TOP(proper(z0)), PROPER(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S, PROPER, TOP

Compound Symbols:

c13, c14, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44, c1, c9, c10, c11, c12, c9, c10, c11, c12, c, c15, c15, c2, c34, c34, c35, c35, c36, c36, c37, c37, c38, c38, c40, c40, c41, c41, c42, c42, c45, c45, c46

327.83/101.54

(65) CdtUnreachableProof (EQUIVALENT transformation)

The following tuples could be removed as they are not reachable from basic start terms:

ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 327.83/101.54
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 327.83/101.54
ACTIVE(first(z0, z1)) → c16(FIRST(active(z0), z1), ACTIVE(z0)) 327.83/101.54
ACTIVE(first(z0, z1)) → c17(FIRST(z0, active(z1)), ACTIVE(z1)) 327.83/101.54
ACTIVE(sqr(s(z0))) → c1(S(add(sqr(z0), dbl(z0)))) 327.83/101.54
ACTIVE(sqr(s(z0))) → c1(ADD(sqr(z0), dbl(z0))) 327.83/101.54
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 327.83/101.54
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 327.83/101.54
ACTIVE(dbl(s(z0))) → c1(S(s(dbl(z0)))) 327.83/101.54
ACTIVE(dbl(s(z0))) → c1(S(dbl(z0))) 327.83/101.54
ACTIVE(dbl(s(z0))) → c1(DBL(z0)) 327.83/101.54
ACTIVE(add(s(z0), z1)) → c1(S(add(z0, z1))) 327.83/101.54
ACTIVE(add(s(z0), z1)) → c1(ADD(z0, z1)) 327.83/101.54
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 327.83/101.54
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 327.83/101.54
ACTIVE(terms(z0)) → c1(SQR(z0)) 327.83/101.54
ACTIVE(terms(z0)) → c1(S(z0)) 327.83/101.54
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.54
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.54
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.54
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.54
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.54
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.54
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.54
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.54
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 327.83/101.54
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 327.83/101.54
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 327.83/101.54
ACTIVE(cons(first(s(z0), cons(z1, z2)), x1)) → c10(CONS(mark(cons(z1, first(z0, z2))), x1), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.54
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 327.83/101.54
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 327.83/101.54
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 327.83/101.54
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 327.83/101.54
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.54
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.54
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.54
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.54
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.54
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.54
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.54
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.54
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.54
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.54
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.54
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.54
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.54
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.54
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.54
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.54
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 327.83/101.54
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.54
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 327.83/101.54
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 327.83/101.54
ACTIVE(terms(sqr(s(z0)))) → c(TERMS(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.54
ACTIVE(terms(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.54
ACTIVE(cons(sqr(s(z0)), x1)) → c(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1)) 327.83/101.54
ACTIVE(cons(sqr(s(z0)), x1)) → c(ACTIVE(sqr(s(z0)))) 327.83/101.54
ACTIVE(recip(sqr(s(z0)))) → c(RECIP(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.54
ACTIVE(recip(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.54
ACTIVE(sqr(sqr(s(z0)))) → c(SQR(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.54
ACTIVE(sqr(sqr(s(z0)))) → c(ACTIVE(sqr(s(z0)))) 327.83/101.54
ACTIVE(dbl(terms(z0))) → c15(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(dbl(add(0, z0))) → c15(DBL(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.54
ACTIVE(dbl(add(s(z0), z1))) → c15(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.54
ACTIVE(dbl(first(0, z0))) → c15(DBL(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.54
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c15(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.54
ACTIVE(dbl(terms(z0))) → c15(DBL(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.54
ACTIVE(dbl(cons(z0, z1))) → c15(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.54
ACTIVE(dbl(recip(z0))) → c15(DBL(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.54
ACTIVE(dbl(sqr(z0))) → c15(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.54
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(dbl(add(z0, z1))) → c15(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.54
ACTIVE(dbl(dbl(z0))) → c15(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.54
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(dbl(first(z0, z1))) → c15(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 327.83/101.54
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 327.83/101.54
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 327.83/101.54
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 327.83/101.54
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 327.83/101.54
ACTIVE(dbl(sqr(0))) → c15(DBL(mark(0))) 327.83/101.54
ACTIVE(dbl(dbl(0))) → c15(DBL(mark(0))) 327.83/101.54
ACTIVE(terms(dbl(s(z0)))) → c2(TERMS(mark(s(s(dbl(z0)))))) 327.83/101.54
ACTIVE(terms(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.54
ACTIVE(cons(dbl(s(z0)), x1)) → c2(CONS(mark(s(s(dbl(z0)))), x1)) 327.83/101.54
ACTIVE(cons(dbl(s(z0)), x1)) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.54
ACTIVE(recip(dbl(s(z0)))) → c2(RECIP(mark(s(s(dbl(z0)))))) 327.83/101.54
ACTIVE(recip(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.54
ACTIVE(sqr(dbl(s(z0)))) → c2(SQR(mark(s(s(dbl(z0)))))) 327.83/101.54
ACTIVE(sqr(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.54
ACTIVE(dbl(sqr(s(z0)))) → c2(DBL(mark(s(add(sqr(z0), dbl(z0)))))) 327.83/101.54
ACTIVE(dbl(sqr(s(z0)))) → c2(ACTIVE(sqr(s(z0)))) 327.83/101.54
ACTIVE(dbl(dbl(s(z0)))) → c2(DBL(mark(s(s(dbl(z0)))))) 327.83/101.54
ACTIVE(dbl(dbl(s(z0)))) → c2(ACTIVE(dbl(s(z0)))) 327.83/101.54
PROPER(terms(terms(z0))) → c34(TERMS(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.54
PROPER(terms(cons(z0, z1))) → c34(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(terms(recip(z0))) → c34(TERMS(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.54
PROPER(terms(sqr(z0))) → c34(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.54
PROPER(terms(s(z0))) → c34(TERMS(s(proper(z0))), PROPER(s(z0))) 327.83/101.54
PROPER(terms(add(z0, z1))) → c34(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.54
PROPER(terms(dbl(z0))) → c34(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.54
PROPER(terms(first(z0, z1))) → c34(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.54
PROPER(terms(0)) → c34(TERMS(ok(0))) 327.83/101.54
PROPER(terms(nil)) → c34(TERMS(ok(nil))) 327.83/101.54
PROPER(cons(x0, terms(z0))) → c35(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.54
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(cons(x0, recip(z0))) → c35(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.54
PROPER(cons(x0, sqr(z0))) → c35(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.54
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.54
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.54
PROPER(cons(x0, dbl(z0))) → c35(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.54
PROPER(cons(x0, first(z0, z1))) → c35(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.54
PROPER(cons(terms(z0), x1)) → c35(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.54
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(cons(recip(z0), x1)) → c35(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.54
PROPER(cons(sqr(z0), x1)) → c35(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.54
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.54
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(cons(dbl(z0), x1)) → c35(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.54
PROPER(cons(first(z0, z1), x1)) → c35(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 327.83/101.54
PROPER(cons(x0, nil)) → c35(CONS(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.54
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 327.83/101.54
PROPER(cons(nil, x1)) → c35(CONS(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.54
PROPER(recip(terms(z0))) → c36(RECIP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.54
PROPER(recip(cons(z0, z1))) → c36(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(recip(recip(z0))) → c36(RECIP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.54
PROPER(recip(sqr(z0))) → c36(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.54
PROPER(recip(s(z0))) → c36(RECIP(s(proper(z0))), PROPER(s(z0))) 327.83/101.54
PROPER(recip(add(z0, z1))) → c36(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.54
PROPER(recip(dbl(z0))) → c36(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.54
PROPER(recip(first(z0, z1))) → c36(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.54
PROPER(recip(0)) → c36(RECIP(ok(0))) 327.83/101.54
PROPER(recip(nil)) → c36(RECIP(ok(nil))) 327.83/101.54
PROPER(sqr(terms(z0))) → c37(SQR(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.54
PROPER(sqr(cons(z0, z1))) → c37(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(sqr(recip(z0))) → c37(SQR(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.54
PROPER(sqr(sqr(z0))) → c37(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.54
PROPER(sqr(s(z0))) → c37(SQR(s(proper(z0))), PROPER(s(z0))) 327.83/101.54
PROPER(sqr(add(z0, z1))) → c37(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.54
PROPER(sqr(dbl(z0))) → c37(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.54
PROPER(sqr(first(z0, z1))) → c37(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.54
PROPER(sqr(0)) → c37(SQR(ok(0))) 327.83/101.54
PROPER(sqr(nil)) → c37(SQR(ok(nil))) 327.83/101.54
PROPER(s(terms(z0))) → c38(S(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.54
PROPER(s(cons(z0, z1))) → c38(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(s(recip(z0))) → c38(S(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.54
PROPER(s(sqr(z0))) → c38(S(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.54
PROPER(s(s(z0))) → c38(S(s(proper(z0))), PROPER(s(z0))) 327.83/101.54
PROPER(s(add(z0, z1))) → c38(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.54
PROPER(s(dbl(z0))) → c38(S(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.54
PROPER(s(first(z0, z1))) → c38(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.54
PROPER(s(0)) → c38(S(ok(0))) 327.83/101.54
PROPER(s(nil)) → c38(S(ok(nil))) 327.83/101.54
PROPER(add(x0, terms(z0))) → c40(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.54
PROPER(add(x0, cons(z0, z1))) → c40(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(add(x0, recip(z0))) → c40(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.54
PROPER(add(x0, sqr(z0))) → c40(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.54
PROPER(add(x0, s(z0))) → c40(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.54
PROPER(add(x0, add(z0, z1))) → c40(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.54
PROPER(add(x0, dbl(z0))) → c40(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.54
PROPER(add(x0, first(z0, z1))) → c40(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.54
PROPER(add(terms(z0), x1)) → c40(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.54
PROPER(add(cons(z0, z1), x1)) → c40(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(add(recip(z0), x1)) → c40(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.54
PROPER(add(sqr(z0), x1)) → c40(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.54
PROPER(add(s(z0), x1)) → c40(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.54
PROPER(add(add(z0, z1), x1)) → c40(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(add(dbl(z0), x1)) → c40(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.54
PROPER(add(first(z0, z1), x1)) → c40(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(add(x0, 0)) → c40(ADD(proper(x0), ok(0)), PROPER(x0)) 327.83/101.54
PROPER(add(x0, nil)) → c40(ADD(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.54
PROPER(add(0, x1)) → c40(ADD(ok(0), proper(x1)), PROPER(x1)) 327.83/101.54
PROPER(add(nil, x1)) → c40(ADD(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.54
PROPER(dbl(terms(z0))) → c41(DBL(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.54
PROPER(dbl(cons(z0, z1))) → c41(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(dbl(recip(z0))) → c41(DBL(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.54
PROPER(dbl(sqr(z0))) → c41(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.54
PROPER(dbl(s(z0))) → c41(DBL(s(proper(z0))), PROPER(s(z0))) 327.83/101.54
PROPER(dbl(add(z0, z1))) → c41(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.54
PROPER(dbl(dbl(z0))) → c41(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.54
PROPER(dbl(first(z0, z1))) → c41(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.54
PROPER(dbl(0)) → c41(DBL(ok(0))) 327.83/101.54
PROPER(dbl(nil)) → c41(DBL(ok(nil))) 327.83/101.54
PROPER(first(x0, terms(z0))) → c42(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 327.83/101.54
PROPER(first(x0, cons(z0, z1))) → c42(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 327.83/101.54
PROPER(first(x0, recip(z0))) → c42(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 327.83/101.54
PROPER(first(x0, sqr(z0))) → c42(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 327.83/101.54
PROPER(first(x0, s(z0))) → c42(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 327.83/101.54
PROPER(first(x0, add(z0, z1))) → c42(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 327.83/101.54
PROPER(first(x0, dbl(z0))) → c42(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 327.83/101.54
PROPER(first(x0, first(z0, z1))) → c42(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 327.83/101.54
PROPER(first(terms(z0), x1)) → c42(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 327.83/101.54
PROPER(first(cons(z0, z1), x1)) → c42(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(first(recip(z0), x1)) → c42(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 327.83/101.54
PROPER(first(sqr(z0), x1)) → c42(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 327.83/101.54
PROPER(first(s(z0), x1)) → c42(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 327.83/101.54
PROPER(first(add(z0, z1), x1)) → c42(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(first(dbl(z0), x1)) → c42(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 327.83/101.54
PROPER(first(first(z0, z1), x1)) → c42(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 327.83/101.54
PROPER(first(x0, 0)) → c42(FIRST(proper(x0), ok(0)), PROPER(x0)) 327.83/101.54
PROPER(first(x0, nil)) → c42(FIRST(proper(x0), ok(nil)), PROPER(x0)) 327.83/101.54
PROPER(first(0, x1)) → c42(FIRST(ok(0), proper(x1)), PROPER(x1)) 327.83/101.54
PROPER(first(nil, x1)) → c42(FIRST(ok(nil), proper(x1)), PROPER(x1)) 327.83/101.54
TOP(mark(terms(z0))) → c45(TOP(terms(proper(z0))), PROPER(terms(z0))) 327.83/101.54
TOP(mark(cons(z0, z1))) → c45(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 327.83/101.54
TOP(mark(recip(z0))) → c45(TOP(recip(proper(z0))), PROPER(recip(z0))) 327.83/101.54
TOP(mark(sqr(z0))) → c45(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 327.83/101.54
TOP(mark(s(z0))) → c45(TOP(s(proper(z0))), PROPER(s(z0))) 327.83/101.54
TOP(mark(add(z0, z1))) → c45(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 327.83/101.54
TOP(mark(dbl(z0))) → c45(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 327.83/101.54
TOP(mark(first(z0, z1))) → c45(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 327.83/101.54
TOP(ok(terms(z0))) → c46(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 327.83/101.54
TOP(ok(sqr(0))) → c46(TOP(mark(0)), ACTIVE(sqr(0))) 327.83/101.54
TOP(ok(sqr(s(z0)))) → c46(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 327.83/101.54
TOP(ok(dbl(0))) → c46(TOP(mark(0)), ACTIVE(dbl(0))) 327.83/101.54
TOP(ok(dbl(s(z0)))) → c46(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 327.83/101.54
TOP(ok(add(0, z0))) → c46(TOP(mark(z0)), ACTIVE(add(0, z0))) 327.83/101.54
TOP(ok(add(s(z0), z1))) → c46(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 327.83/101.54
TOP(ok(first(0, z0))) → c46(TOP(mark(nil)), ACTIVE(first(0, z0))) 327.83/101.54
TOP(ok(first(s(z0), cons(z1, z2)))) → c46(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 327.83/101.54
TOP(ok(terms(z0))) → c46(TOP(terms(active(z0))), ACTIVE(terms(z0))) 327.83/101.54
TOP(ok(cons(z0, z1))) → c46(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 327.83/101.54
TOP(ok(recip(z0))) → c46(TOP(recip(active(z0))), ACTIVE(recip(z0))) 327.83/101.54
TOP(ok(sqr(z0))) → c46(TOP(sqr(active(z0))), ACTIVE(sqr(z0))) 327.83/101.54
TOP(ok(add(z0, z1))) → c46(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 327.83/101.54
TOP(ok(add(z0, z1))) → c46(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 327.83/101.54
TOP(ok(dbl(z0))) → c46(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 327.83/101.54
TOP(ok(first(z0, z1))) → c46(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 327.83/101.54
TOP(ok(first(z0, z1))) → c46(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

327.83/101.54

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.54
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.54
active(first(0, z0)) → mark(nil) 327.83/101.54
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.54
active(terms(z0)) → terms(active(z0)) 327.83/101.54
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.54
active(recip(z0)) → recip(active(z0)) 327.83/101.54
active(sqr(z0)) → sqr(active(z0)) 327.83/101.54
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.54
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.54
active(dbl(z0)) → dbl(active(z0)) 327.83/101.54
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.54
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.54
terms(mark(z0)) → mark(terms(z0)) 327.83/101.54
terms(ok(z0)) → ok(terms(z0)) 327.83/101.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.54
recip(mark(z0)) → mark(recip(z0)) 327.83/101.54
recip(ok(z0)) → ok(recip(z0)) 327.83/101.54
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.54
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.54
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.54
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.54
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.54
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.54
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.54
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.54
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.54
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.54
proper(terms(z0)) → terms(proper(z0)) 327.83/101.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.54
proper(recip(z0)) → recip(proper(z0)) 327.83/101.54
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.54
proper(s(z0)) → s(proper(z0)) 327.83/101.54
proper(0) → ok(0) 327.83/101.54
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.54
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.54
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.54
proper(nil) → ok(nil) 327.83/101.54
s(ok(z0)) → ok(s(z0)) 327.83/101.54
top(mark(z0)) → top(proper(z0)) 327.83/101.54
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0)) 327.83/101.54
TOP(mark(0)) → c45(TOP(ok(0))) 327.83/101.54
TOP(mark(nil)) → c45(TOP(ok(nil)))

S tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

K tuples:none
Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44, c45

327.83/101.54

(67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

327.83/101.54

(68) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.54
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.54
active(first(0, z0)) → mark(nil) 327.83/101.54
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.54
active(terms(z0)) → terms(active(z0)) 327.83/101.54
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.54
active(recip(z0)) → recip(active(z0)) 327.83/101.54
active(sqr(z0)) → sqr(active(z0)) 327.83/101.54
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.54
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.54
active(dbl(z0)) → dbl(active(z0)) 327.83/101.54
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.54
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.54
terms(mark(z0)) → mark(terms(z0)) 327.83/101.54
terms(ok(z0)) → ok(terms(z0)) 327.83/101.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.54
recip(mark(z0)) → mark(recip(z0)) 327.83/101.54
recip(ok(z0)) → ok(recip(z0)) 327.83/101.54
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.54
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.54
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.54
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.54
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.54
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.54
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.54
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.54
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.54
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.54
proper(terms(z0)) → terms(proper(z0)) 327.83/101.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.54
proper(recip(z0)) → recip(proper(z0)) 327.83/101.54
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.54
proper(s(z0)) → s(proper(z0)) 327.83/101.54
proper(0) → ok(0) 327.83/101.54
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.54
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.54
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.54
proper(nil) → ok(nil) 327.83/101.54
s(ok(z0)) → ok(s(z0)) 327.83/101.54
top(mark(z0)) → top(proper(z0)) 327.83/101.54
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0)) 327.83/101.54
TOP(mark(0)) → c45 327.83/101.54
TOP(mark(nil)) → c45

S tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

K tuples:none
Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44, c45

327.83/101.54

(69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing nodes:

TOP(mark(nil)) → c45 327.83/101.54
TOP(mark(0)) → c45

327.83/101.54

(70) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.54
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.54
active(first(0, z0)) → mark(nil) 327.83/101.54
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.54
active(terms(z0)) → terms(active(z0)) 327.83/101.54
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.54
active(recip(z0)) → recip(active(z0)) 327.83/101.54
active(sqr(z0)) → sqr(active(z0)) 327.83/101.54
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.54
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.54
active(dbl(z0)) → dbl(active(z0)) 327.83/101.54
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.54
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.54
terms(mark(z0)) → mark(terms(z0)) 327.83/101.54
terms(ok(z0)) → ok(terms(z0)) 327.83/101.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.54
recip(mark(z0)) → mark(recip(z0)) 327.83/101.54
recip(ok(z0)) → ok(recip(z0)) 327.83/101.54
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.54
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.54
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.54
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.54
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.54
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.54
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.54
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.54
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.54
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.54
proper(terms(z0)) → terms(proper(z0)) 327.83/101.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.54
proper(recip(z0)) → recip(proper(z0)) 327.83/101.54
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.54
proper(s(z0)) → s(proper(z0)) 327.83/101.54
proper(0) → ok(0) 327.83/101.54
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.54
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.54
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.54
proper(nil) → ok(nil) 327.83/101.54
s(ok(z0)) → ok(s(z0)) 327.83/101.54
top(mark(z0)) → top(proper(z0)) 327.83/101.54
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

S tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

K tuples:none
Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.54

(71) 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.

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.54

POL(ADD(x₁, x₂)) = 0 327.83/101.54
POL(CONS(x₁, x₂)) = x₂ 327.83/101.54
POL(DBL(x₁)) = 0 327.83/101.54
POL(FIRST(x₁, x₂)) = x₂ 327.83/101.54
POL(RECIP(x₁)) = 0 327.83/101.54
POL(S(x₁)) = 0 327.83/101.54
POL(SQR(x₁)) = 0 327.83/101.54
POL(TERMS(x₁)) = 0 327.83/101.54
POL(c18(x₁)) = x₁ 327.83/101.54
POL(c19(x₁)) = x₁ 327.83/101.54
POL(c20(x₁)) = x₁ 327.83/101.54
POL(c21(x₁)) = x₁ 327.83/101.54
POL(c22(x₁)) = x₁ 327.83/101.54
POL(c23(x₁)) = x₁ 327.83/101.54
POL(c24(x₁)) = x₁ 327.83/101.54
POL(c25(x₁)) = x₁ 327.83/101.54
POL(c26(x₁)) = x₁ 327.83/101.54
POL(c27(x₁)) = x₁ 327.83/101.54
POL(c28(x₁)) = x₁ 327.83/101.54
POL(c29(x₁)) = x₁ 327.83/101.54
POL(c30(x₁)) = x₁ 327.83/101.54
POL(c31(x₁)) = x₁ 327.83/101.54
POL(c32(x₁)) = x₁ 327.83/101.54
POL(c33(x₁)) = x₁ 327.83/101.54
POL(c44(x₁)) = x₁ 327.83/101.54
POL(mark(x₁)) = [1] + x₁ 327.83/101.54
POL(ok(x₁)) = x₁

327.83/101.54

(72) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.54
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.54
active(first(0, z0)) → mark(nil) 327.83/101.54
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.54
active(terms(z0)) → terms(active(z0)) 327.83/101.54
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.54
active(recip(z0)) → recip(active(z0)) 327.83/101.54
active(sqr(z0)) → sqr(active(z0)) 327.83/101.54
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.54
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.54
active(dbl(z0)) → dbl(active(z0)) 327.83/101.54
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.54
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.54
terms(mark(z0)) → mark(terms(z0)) 327.83/101.54
terms(ok(z0)) → ok(terms(z0)) 327.83/101.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.54
recip(mark(z0)) → mark(recip(z0)) 327.83/101.54
recip(ok(z0)) → ok(recip(z0)) 327.83/101.54
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.54
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.54
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.54
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.54
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.54
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.54
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.54
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.54
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.54
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.54
proper(terms(z0)) → terms(proper(z0)) 327.83/101.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.54
proper(recip(z0)) → recip(proper(z0)) 327.83/101.54
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.54
proper(s(z0)) → s(proper(z0)) 327.83/101.54
proper(0) → ok(0) 327.83/101.54
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.54
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.54
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.54
proper(nil) → ok(nil) 327.83/101.54
s(ok(z0)) → ok(s(z0)) 327.83/101.54
top(mark(z0)) → top(proper(z0)) 327.83/101.54
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

S tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.54

(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.

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.54

POL(ADD(x₁, x₂)) = 0 327.83/101.54
POL(CONS(x₁, x₂)) = 0 327.83/101.54
POL(DBL(x₁)) = 0 327.83/101.54
POL(FIRST(x₁, x₂)) = 0 327.83/101.54
POL(RECIP(x₁)) = 0 327.83/101.54
POL(S(x₁)) = 0 327.83/101.54
POL(SQR(x₁)) = 0 327.83/101.54
POL(TERMS(x₁)) = [2]x₁ 327.83/101.54
POL(c18(x₁)) = x₁ 327.83/101.54
POL(c19(x₁)) = x₁ 327.83/101.54
POL(c20(x₁)) = x₁ 327.83/101.54
POL(c21(x₁)) = x₁ 327.83/101.54
POL(c22(x₁)) = x₁ 327.83/101.54
POL(c23(x₁)) = x₁ 327.83/101.54
POL(c24(x₁)) = x₁ 327.83/101.54
POL(c25(x₁)) = x₁ 327.83/101.54
POL(c26(x₁)) = x₁ 327.83/101.54
POL(c27(x₁)) = x₁ 327.83/101.54
POL(c28(x₁)) = x₁ 327.83/101.54
POL(c29(x₁)) = x₁ 327.83/101.54
POL(c30(x₁)) = x₁ 327.83/101.54
POL(c31(x₁)) = x₁ 327.83/101.54
POL(c32(x₁)) = x₁ 327.83/101.54
POL(c33(x₁)) = x₁ 327.83/101.54
POL(c44(x₁)) = x₁ 327.83/101.54
POL(mark(x₁)) = [1] + x₁ 327.83/101.54
POL(ok(x₁)) = [1] + x₁

327.83/101.54

(74) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.54
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.54
active(first(0, z0)) → mark(nil) 327.83/101.54
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.54
active(terms(z0)) → terms(active(z0)) 327.83/101.54
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.54
active(recip(z0)) → recip(active(z0)) 327.83/101.54
active(sqr(z0)) → sqr(active(z0)) 327.83/101.54
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.54
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.54
active(dbl(z0)) → dbl(active(z0)) 327.83/101.54
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.54
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.54
terms(mark(z0)) → mark(terms(z0)) 327.83/101.54
terms(ok(z0)) → ok(terms(z0)) 327.83/101.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.54
recip(mark(z0)) → mark(recip(z0)) 327.83/101.54
recip(ok(z0)) → ok(recip(z0)) 327.83/101.54
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.54
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.54
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.54
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.54
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.54
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.54
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.54
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.54
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.54
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.54
proper(terms(z0)) → terms(proper(z0)) 327.83/101.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.54
proper(recip(z0)) → recip(proper(z0)) 327.83/101.54
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.54
proper(s(z0)) → s(proper(z0)) 327.83/101.54
proper(0) → ok(0) 327.83/101.54
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.54
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.54
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.54
proper(nil) → ok(nil) 327.83/101.54
s(ok(z0)) → ok(s(z0)) 327.83/101.54
top(mark(z0)) → top(proper(z0)) 327.83/101.54
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

S tuples:

CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.54

(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.

RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.54

POL(ADD(x₁, x₂)) = 0 327.83/101.54
POL(CONS(x₁, x₂)) = 0 327.83/101.54
POL(DBL(x₁)) = 0 327.83/101.54
POL(FIRST(x₁, x₂)) = 0 327.83/101.54
POL(RECIP(x₁)) = x₁ 327.83/101.54
POL(S(x₁)) = 0 327.83/101.54
POL(SQR(x₁)) = 0 327.83/101.54
POL(TERMS(x₁)) = [5]x₁ 327.83/101.54
POL(c18(x₁)) = x₁ 327.83/101.54
POL(c19(x₁)) = x₁ 327.83/101.54
POL(c20(x₁)) = x₁ 327.83/101.54
POL(c21(x₁)) = x₁ 327.83/101.54
POL(c22(x₁)) = x₁ 327.83/101.54
POL(c23(x₁)) = x₁ 327.83/101.54
POL(c24(x₁)) = x₁ 327.83/101.54
POL(c25(x₁)) = x₁ 327.83/101.54
POL(c26(x₁)) = x₁ 327.83/101.54
POL(c27(x₁)) = x₁ 327.83/101.54
POL(c28(x₁)) = x₁ 327.83/101.54
POL(c29(x₁)) = x₁ 327.83/101.54
POL(c30(x₁)) = x₁ 327.83/101.54
POL(c31(x₁)) = x₁ 327.83/101.54
POL(c32(x₁)) = x₁ 327.83/101.54
POL(c33(x₁)) = x₁ 327.83/101.54
POL(c44(x₁)) = x₁ 327.83/101.54
POL(mark(x₁)) = [1] + x₁ 327.83/101.54
POL(ok(x₁)) = [1] + x₁

327.83/101.54

(76) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.54
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.54
active(first(0, z0)) → mark(nil) 327.83/101.54
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.54
active(terms(z0)) → terms(active(z0)) 327.83/101.54
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.54
active(recip(z0)) → recip(active(z0)) 327.83/101.54
active(sqr(z0)) → sqr(active(z0)) 327.83/101.54
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.54
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.54
active(dbl(z0)) → dbl(active(z0)) 327.83/101.54
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.54
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.54
terms(mark(z0)) → mark(terms(z0)) 327.83/101.54
terms(ok(z0)) → ok(terms(z0)) 327.83/101.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.54
recip(mark(z0)) → mark(recip(z0)) 327.83/101.54
recip(ok(z0)) → ok(recip(z0)) 327.83/101.54
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.54
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.54
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.54
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.54
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.54
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.54
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.54
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.54
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.54
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.54
proper(terms(z0)) → terms(proper(z0)) 327.83/101.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.54
proper(recip(z0)) → recip(proper(z0)) 327.83/101.54
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.54
proper(s(z0)) → s(proper(z0)) 327.83/101.54
proper(0) → ok(0) 327.83/101.54
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.54
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.54
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.54
proper(nil) → ok(nil) 327.83/101.54
s(ok(z0)) → ok(s(z0)) 327.83/101.54
top(mark(z0)) → top(proper(z0)) 327.83/101.54
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

S tuples:

CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.54

(77) 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.

DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.54

POL(ADD(x₁, x₂)) = 0 327.83/101.54
POL(CONS(x₁, x₂)) = 0 327.83/101.54
POL(DBL(x₁)) = x₁ 327.83/101.54
POL(FIRST(x₁, x₂)) = x₁ 327.83/101.54
POL(RECIP(x₁)) = [3]x₁ 327.83/101.54
POL(S(x₁)) = 0 327.83/101.54
POL(SQR(x₁)) = 0 327.83/101.54
POL(TERMS(x₁)) = [3]x₁ 327.83/101.54
POL(c18(x₁)) = x₁ 327.83/101.54
POL(c19(x₁)) = x₁ 327.83/101.54
POL(c20(x₁)) = x₁ 327.83/101.54
POL(c21(x₁)) = x₁ 327.83/101.54
POL(c22(x₁)) = x₁ 327.83/101.54
POL(c23(x₁)) = x₁ 327.83/101.54
POL(c24(x₁)) = x₁ 327.83/101.54
POL(c25(x₁)) = x₁ 327.83/101.54
POL(c26(x₁)) = x₁ 327.83/101.54
POL(c27(x₁)) = x₁ 327.83/101.54
POL(c28(x₁)) = x₁ 327.83/101.54
POL(c29(x₁)) = x₁ 327.83/101.54
POL(c30(x₁)) = x₁ 327.83/101.54
POL(c31(x₁)) = x₁ 327.83/101.54
POL(c32(x₁)) = x₁ 327.83/101.54
POL(c33(x₁)) = x₁ 327.83/101.54
POL(c44(x₁)) = x₁ 327.83/101.54
POL(mark(x₁)) = [1] + x₁ 327.83/101.54
POL(ok(x₁)) = [2] + x₁

327.83/101.54

(78) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.54
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.54
active(first(0, z0)) → mark(nil) 327.83/101.54
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.54
active(terms(z0)) → terms(active(z0)) 327.83/101.54
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.54
active(recip(z0)) → recip(active(z0)) 327.83/101.54
active(sqr(z0)) → sqr(active(z0)) 327.83/101.54
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.54
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.54
active(dbl(z0)) → dbl(active(z0)) 327.83/101.54
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.54
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.54
terms(mark(z0)) → mark(terms(z0)) 327.83/101.54
terms(ok(z0)) → ok(terms(z0)) 327.83/101.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.54
recip(mark(z0)) → mark(recip(z0)) 327.83/101.54
recip(ok(z0)) → ok(recip(z0)) 327.83/101.54
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.54
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.54
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.54
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.54
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.54
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.54
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.54
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.54
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.54
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.54
proper(terms(z0)) → terms(proper(z0)) 327.83/101.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.54
proper(recip(z0)) → recip(proper(z0)) 327.83/101.54
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.54
proper(s(z0)) → s(proper(z0)) 327.83/101.54
proper(0) → ok(0) 327.83/101.54
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.54
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.54
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.54
proper(nil) → ok(nil) 327.83/101.54
s(ok(z0)) → ok(s(z0)) 327.83/101.54
top(mark(z0)) → top(proper(z0)) 327.83/101.54
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

S tuples:

CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.54

(79) 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) → c20(CONS(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.54

POL(ADD(x₁, x₂)) = 0 327.83/101.54
POL(CONS(x₁, x₂)) = [2]x₁ + x₂ 327.83/101.54
POL(DBL(x₁)) = [3]x₁ 327.83/101.54
POL(FIRST(x₁, x₂)) = [5]x₁ + [5]x₂ 327.83/101.54
POL(RECIP(x₁)) = [5]x₁ 327.83/101.54
POL(S(x₁)) = 0 327.83/101.54
POL(SQR(x₁)) = 0 327.83/101.54
POL(TERMS(x₁)) = [3]x₁ 327.83/101.54
POL(c18(x₁)) = x₁ 327.83/101.54
POL(c19(x₁)) = x₁ 327.83/101.54
POL(c20(x₁)) = x₁ 327.83/101.54
POL(c21(x₁)) = x₁ 327.83/101.54
POL(c22(x₁)) = x₁ 327.83/101.54
POL(c23(x₁)) = x₁ 327.83/101.54
POL(c24(x₁)) = x₁ 327.83/101.54
POL(c25(x₁)) = x₁ 327.83/101.54
POL(c26(x₁)) = x₁ 327.83/101.54
POL(c27(x₁)) = x₁ 327.83/101.54
POL(c28(x₁)) = x₁ 327.83/101.54
POL(c29(x₁)) = x₁ 327.83/101.54
POL(c30(x₁)) = x₁ 327.83/101.54
POL(c31(x₁)) = x₁ 327.83/101.54
POL(c32(x₁)) = x₁ 327.83/101.54
POL(c33(x₁)) = x₁ 327.83/101.54
POL(c44(x₁)) = x₁ 327.83/101.54
POL(mark(x₁)) = [1] + x₁ 327.83/101.54
POL(ok(x₁)) = x₁

327.83/101.54

(80) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.54
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.54
active(first(0, z0)) → mark(nil) 327.83/101.54
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.54
active(terms(z0)) → terms(active(z0)) 327.83/101.54
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.54
active(recip(z0)) → recip(active(z0)) 327.83/101.54
active(sqr(z0)) → sqr(active(z0)) 327.83/101.54
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.54
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.54
active(dbl(z0)) → dbl(active(z0)) 327.83/101.54
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.54
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.54
terms(mark(z0)) → mark(terms(z0)) 327.83/101.54
terms(ok(z0)) → ok(terms(z0)) 327.83/101.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.54
recip(mark(z0)) → mark(recip(z0)) 327.83/101.54
recip(ok(z0)) → ok(recip(z0)) 327.83/101.54
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.54
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.54
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.54
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.54
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.54
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.54
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.54
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.54
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.54
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.54
proper(terms(z0)) → terms(proper(z0)) 327.83/101.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.54
proper(recip(z0)) → recip(proper(z0)) 327.83/101.54
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.54
proper(s(z0)) → s(proper(z0)) 327.83/101.54
proper(0) → ok(0) 327.83/101.54
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.54
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.54
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.54
proper(nil) → ok(nil) 327.83/101.54
s(ok(z0)) → ok(s(z0)) 327.83/101.54
top(mark(z0)) → top(proper(z0)) 327.83/101.54
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

S tuples:

CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.54

(81) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.54

POL(ADD(x₁, x₂)) = 0 327.83/101.54
POL(CONS(x₁, x₂)) = x₁ 327.83/101.54
POL(DBL(x₁)) = [5]x₁ 327.83/101.54
POL(FIRST(x₁, x₂)) = [3]x₁ + [5]x₂ 327.83/101.54
POL(RECIP(x₁)) = [3]x₁ 327.83/101.54
POL(S(x₁)) = 0 327.83/101.54
POL(SQR(x₁)) = 0 327.83/101.54
POL(TERMS(x₁)) = [5]x₁ 327.83/101.54
POL(c18(x₁)) = x₁ 327.83/101.54
POL(c19(x₁)) = x₁ 327.83/101.54
POL(c20(x₁)) = x₁ 327.83/101.54
POL(c21(x₁)) = x₁ 327.83/101.54
POL(c22(x₁)) = x₁ 327.83/101.54
POL(c23(x₁)) = x₁ 327.83/101.54
POL(c24(x₁)) = x₁ 327.83/101.54
POL(c25(x₁)) = x₁ 327.83/101.54
POL(c26(x₁)) = x₁ 327.83/101.54
POL(c27(x₁)) = x₁ 327.83/101.54
POL(c28(x₁)) = x₁ 327.83/101.54
POL(c29(x₁)) = x₁ 327.83/101.54
POL(c30(x₁)) = x₁ 327.83/101.54
POL(c31(x₁)) = x₁ 327.83/101.54
POL(c32(x₁)) = x₁ 327.83/101.54
POL(c33(x₁)) = x₁ 327.83/101.54
POL(c44(x₁)) = x₁ 327.83/101.54
POL(mark(x₁)) = x₁ 327.83/101.54
POL(ok(x₁)) = [2] + x₁

327.83/101.54

(82) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.54
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.54
active(first(0, z0)) → mark(nil) 327.83/101.54
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.54
active(terms(z0)) → terms(active(z0)) 327.83/101.54
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.54
active(recip(z0)) → recip(active(z0)) 327.83/101.54
active(sqr(z0)) → sqr(active(z0)) 327.83/101.54
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.54
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.54
active(dbl(z0)) → dbl(active(z0)) 327.83/101.54
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.54
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.54
terms(mark(z0)) → mark(terms(z0)) 327.83/101.54
terms(ok(z0)) → ok(terms(z0)) 327.83/101.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.54
recip(mark(z0)) → mark(recip(z0)) 327.83/101.54
recip(ok(z0)) → ok(recip(z0)) 327.83/101.54
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.54
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.54
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.54
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.54
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.54
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.54
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.54
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.54
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.54
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.54
proper(terms(z0)) → terms(proper(z0)) 327.83/101.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.54
proper(recip(z0)) → recip(proper(z0)) 327.83/101.54
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.54
proper(s(z0)) → s(proper(z0)) 327.83/101.54
proper(0) → ok(0) 327.83/101.54
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.54
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.54
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.54
proper(nil) → ok(nil) 327.83/101.54
s(ok(z0)) → ok(s(z0)) 327.83/101.54
top(mark(z0)) → top(proper(z0)) 327.83/101.54
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

S tuples:

SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.54

(83) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

ADD(mark(z0), z1) → c26(ADD(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.54

POL(ADD(x₁, x₂)) = x₁ 327.83/101.54
POL(CONS(x₁, x₂)) = [5]x₁ + [5]x₂ 327.83/101.54
POL(DBL(x₁)) = [3]x₁ 327.83/101.54
POL(FIRST(x₁, x₂)) = [5]x₁ + [5]x₂ 327.83/101.54
POL(RECIP(x₁)) = [3]x₁ 327.83/101.54
POL(S(x₁)) = 0 327.83/101.54
POL(SQR(x₁)) = 0 327.83/101.54
POL(TERMS(x₁)) = [3]x₁ 327.83/101.54
POL(c18(x₁)) = x₁ 327.83/101.54
POL(c19(x₁)) = x₁ 327.83/101.54
POL(c20(x₁)) = x₁ 327.83/101.54
POL(c21(x₁)) = x₁ 327.83/101.54
POL(c22(x₁)) = x₁ 327.83/101.54
POL(c23(x₁)) = x₁ 327.83/101.54
POL(c24(x₁)) = x₁ 327.83/101.54
POL(c25(x₁)) = x₁ 327.83/101.54
POL(c26(x₁)) = x₁ 327.83/101.54
POL(c27(x₁)) = x₁ 327.83/101.54
POL(c28(x₁)) = x₁ 327.83/101.54
POL(c29(x₁)) = x₁ 327.83/101.54
POL(c30(x₁)) = x₁ 327.83/101.54
POL(c31(x₁)) = x₁ 327.83/101.54
POL(c32(x₁)) = x₁ 327.83/101.54
POL(c33(x₁)) = x₁ 327.83/101.54
POL(c44(x₁)) = x₁ 327.83/101.54
POL(mark(x₁)) = [1] + x₁ 327.83/101.54
POL(ok(x₁)) = x₁

327.83/101.54

(84) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.54
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.54
active(first(0, z0)) → mark(nil) 327.83/101.54
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.54
active(terms(z0)) → terms(active(z0)) 327.83/101.54
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.54
active(recip(z0)) → recip(active(z0)) 327.83/101.54
active(sqr(z0)) → sqr(active(z0)) 327.83/101.54
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.54
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.54
active(dbl(z0)) → dbl(active(z0)) 327.83/101.54
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.54
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.54
terms(mark(z0)) → mark(terms(z0)) 327.83/101.54
terms(ok(z0)) → ok(terms(z0)) 327.83/101.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.54
recip(mark(z0)) → mark(recip(z0)) 327.83/101.54
recip(ok(z0)) → ok(recip(z0)) 327.83/101.54
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.54
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.54
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.54
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.54
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.54
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.54
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.54
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.54
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.54
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.54
proper(terms(z0)) → terms(proper(z0)) 327.83/101.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.54
proper(recip(z0)) → recip(proper(z0)) 327.83/101.54
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.54
proper(s(z0)) → s(proper(z0)) 327.83/101.54
proper(0) → ok(0) 327.83/101.54
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.54
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.54
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.54
proper(nil) → ok(nil) 327.83/101.54
s(ok(z0)) → ok(s(z0)) 327.83/101.54
top(mark(z0)) → top(proper(z0)) 327.83/101.54
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

S tuples:

SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.54

(85) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

ADD(z0, mark(z1)) → c27(ADD(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.54

POL(ADD(x₁, x₂)) = x₂ 327.83/101.54
POL(CONS(x₁, x₂)) = [3]x₁ + [5]x₂ 327.83/101.54
POL(DBL(x₁)) = [3]x₁ 327.83/101.54
POL(FIRST(x₁, x₂)) = [5]x₁ + [3]x₂ 327.83/101.54
POL(RECIP(x₁)) = [5]x₁ 327.83/101.54
POL(S(x₁)) = 0 327.83/101.54
POL(SQR(x₁)) = 0 327.83/101.54
POL(TERMS(x₁)) = [3]x₁ 327.83/101.54
POL(c18(x₁)) = x₁ 327.83/101.54
POL(c19(x₁)) = x₁ 327.83/101.54
POL(c20(x₁)) = x₁ 327.83/101.54
POL(c21(x₁)) = x₁ 327.83/101.54
POL(c22(x₁)) = x₁ 327.83/101.54
POL(c23(x₁)) = x₁ 327.83/101.54
POL(c24(x₁)) = x₁ 327.83/101.54
POL(c25(x₁)) = x₁ 327.83/101.54
POL(c26(x₁)) = x₁ 327.83/101.54
POL(c27(x₁)) = x₁ 327.83/101.54
POL(c28(x₁)) = x₁ 327.83/101.54
POL(c29(x₁)) = x₁ 327.83/101.54
POL(c30(x₁)) = x₁ 327.83/101.54
POL(c31(x₁)) = x₁ 327.83/101.54
POL(c32(x₁)) = x₁ 327.83/101.54
POL(c33(x₁)) = x₁ 327.83/101.54
POL(c44(x₁)) = x₁ 327.83/101.54
POL(mark(x₁)) = [1] + x₁ 327.83/101.54
POL(ok(x₁)) = x₁

327.83/101.54

(86) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.54
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.54
active(first(0, z0)) → mark(nil) 327.83/101.54
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.54
active(terms(z0)) → terms(active(z0)) 327.83/101.54
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.54
active(recip(z0)) → recip(active(z0)) 327.83/101.54
active(sqr(z0)) → sqr(active(z0)) 327.83/101.54
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.54
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.54
active(dbl(z0)) → dbl(active(z0)) 327.83/101.54
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.54
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.54
terms(mark(z0)) → mark(terms(z0)) 327.83/101.54
terms(ok(z0)) → ok(terms(z0)) 327.83/101.54
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.54
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.54
recip(mark(z0)) → mark(recip(z0)) 327.83/101.54
recip(ok(z0)) → ok(recip(z0)) 327.83/101.54
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.54
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.54
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.54
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.54
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.54
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.54
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.54
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.54
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.54
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.54
proper(terms(z0)) → terms(proper(z0)) 327.83/101.54
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.54
proper(recip(z0)) → recip(proper(z0)) 327.83/101.54
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.54
proper(s(z0)) → s(proper(z0)) 327.83/101.54
proper(0) → ok(0) 327.83/101.54
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.54
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.54
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.54
proper(nil) → ok(nil) 327.83/101.54
s(ok(z0)) → ok(s(z0)) 327.83/101.54
top(mark(z0)) → top(proper(z0)) 327.83/101.54
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

S tuples:

SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.54

(87) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

S(ok(z0)) → c44(S(z0))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.54
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.54
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.54
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.54
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.54
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.54
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.54
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.54
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.54
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.54
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.54
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.54
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.54
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.54
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.54
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.54
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.54

POL(ADD(x₁, x₂)) = 0 327.83/101.54
POL(CONS(x₁, x₂)) = [5]x₁ + [5]x₂ 327.83/101.54
POL(DBL(x₁)) = [3]x₁ 327.83/101.54
POL(FIRST(x₁, x₂)) = [3]x₁ + [5]x₂ 327.83/101.54
POL(RECIP(x₁)) = [5]x₁ 327.83/101.54
POL(S(x₁)) = x₁ 327.83/101.54
POL(SQR(x₁)) = 0 327.83/101.54
POL(TERMS(x₁)) = [5]x₁ 327.83/101.54
POL(c18(x₁)) = x₁ 327.83/101.54
POL(c19(x₁)) = x₁ 327.83/101.54
POL(c20(x₁)) = x₁ 327.83/101.54
POL(c21(x₁)) = x₁ 327.83/101.54
POL(c22(x₁)) = x₁ 327.83/101.54
POL(c23(x₁)) = x₁ 327.83/101.54
POL(c24(x₁)) = x₁ 327.83/101.54
POL(c25(x₁)) = x₁ 327.83/101.54
POL(c26(x₁)) = x₁ 327.83/101.54
POL(c27(x₁)) = x₁ 327.83/101.54
POL(c28(x₁)) = x₁ 327.83/101.54
POL(c29(x₁)) = x₁ 327.83/101.54
POL(c30(x₁)) = x₁ 327.83/101.54
POL(c31(x₁)) = x₁ 327.83/101.54
POL(c32(x₁)) = x₁ 327.83/101.54
POL(c33(x₁)) = x₁ 327.83/101.54
POL(c44(x₁)) = x₁ 327.83/101.54
POL(mark(x₁)) = [1] + x₁ 327.83/101.54
POL(ok(x₁)) = [1] + x₁

327.83/101.54

(88) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.54
active(sqr(0)) → mark(0) 327.83/101.54
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.54
active(dbl(0)) → mark(0) 327.83/101.54
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.54
active(add(0, z0)) → mark(z0) 327.83/101.55
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.55
active(first(0, z0)) → mark(nil) 327.83/101.55
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.55
active(terms(z0)) → terms(active(z0)) 327.83/101.55
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.55
active(recip(z0)) → recip(active(z0)) 327.83/101.55
active(sqr(z0)) → sqr(active(z0)) 327.83/101.55
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.55
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.55
active(dbl(z0)) → dbl(active(z0)) 327.83/101.55
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.55
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.55
terms(mark(z0)) → mark(terms(z0)) 327.83/101.55
terms(ok(z0)) → ok(terms(z0)) 327.83/101.55
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.55
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.55
recip(mark(z0)) → mark(recip(z0)) 327.83/101.55
recip(ok(z0)) → ok(recip(z0)) 327.83/101.55
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.55
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.55
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.55
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.55
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.55
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.55
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.55
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.55
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.55
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.55
proper(terms(z0)) → terms(proper(z0)) 327.83/101.55
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.55
proper(recip(z0)) → recip(proper(z0)) 327.83/101.55
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.55
proper(s(z0)) → s(proper(z0)) 327.83/101.55
proper(0) → ok(0) 327.83/101.55
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.55
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.55
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.55
proper(nil) → ok(nil) 327.83/101.55
s(ok(z0)) → ok(s(z0)) 327.83/101.55
top(mark(z0)) → top(proper(z0)) 327.83/101.55
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.55
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.55
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.55
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.55
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.55
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.55
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.55
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.55
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.55
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.55
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.55
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.55
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.55
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.55
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.55
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.55
S(ok(z0)) → c44(S(z0))

S tuples:

SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.55
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.55
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1))

K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.55
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.55
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.55
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.55
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.55
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.55
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.55
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.55
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.55
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.55
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.55
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.55
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.55
S(ok(z0)) → c44(S(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.55

(89) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

SQR(mark(z0)) → c24(SQR(z0))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.55
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.55
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.55
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.55
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.55
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.55
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.55
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.55
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.55
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.55
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.55
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.55
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.55
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.55
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.55
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.55
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.55

POL(ADD(x₁, x₂)) = x₁ + x₂ 327.83/101.55
POL(CONS(x₁, x₂)) = [5]x₁ + [5]x₂ 327.83/101.55
POL(DBL(x₁)) = [3]x₁ 327.83/101.55
POL(FIRST(x₁, x₂)) = [5]x₁ + [5]x₂ 327.83/101.55
POL(RECIP(x₁)) = [5]x₁ 327.83/101.55
POL(S(x₁)) = [5]x₁ 327.83/101.55
POL(SQR(x₁)) = [2]x₁ 327.83/101.55
POL(TERMS(x₁)) = [3]x₁ 327.83/101.55
POL(c18(x₁)) = x₁ 327.83/101.55
POL(c19(x₁)) = x₁ 327.83/101.55
POL(c20(x₁)) = x₁ 327.83/101.55
POL(c21(x₁)) = x₁ 327.83/101.55
POL(c22(x₁)) = x₁ 327.83/101.55
POL(c23(x₁)) = x₁ 327.83/101.55
POL(c24(x₁)) = x₁ 327.83/101.55
POL(c25(x₁)) = x₁ 327.83/101.55
POL(c26(x₁)) = x₁ 327.83/101.55
POL(c27(x₁)) = x₁ 327.83/101.55
POL(c28(x₁)) = x₁ 327.83/101.55
POL(c29(x₁)) = x₁ 327.83/101.55
POL(c30(x₁)) = x₁ 327.83/101.55
POL(c31(x₁)) = x₁ 327.83/101.55
POL(c32(x₁)) = x₁ 327.83/101.55
POL(c33(x₁)) = x₁ 327.83/101.55
POL(c44(x₁)) = x₁ 327.83/101.55
POL(mark(x₁)) = [1] + x₁ 327.83/101.55
POL(ok(x₁)) = x₁

327.83/101.55

(90) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.55
active(sqr(0)) → mark(0) 327.83/101.55
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.55
active(dbl(0)) → mark(0) 327.83/101.55
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.55
active(add(0, z0)) → mark(z0) 327.83/101.55
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.55
active(first(0, z0)) → mark(nil) 327.83/101.55
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.55
active(terms(z0)) → terms(active(z0)) 327.83/101.55
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.55
active(recip(z0)) → recip(active(z0)) 327.83/101.55
active(sqr(z0)) → sqr(active(z0)) 327.83/101.55
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.55
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.55
active(dbl(z0)) → dbl(active(z0)) 327.83/101.55
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.55
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.55
terms(mark(z0)) → mark(terms(z0)) 327.83/101.55
terms(ok(z0)) → ok(terms(z0)) 327.83/101.55
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.55
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.55
recip(mark(z0)) → mark(recip(z0)) 327.83/101.55
recip(ok(z0)) → ok(recip(z0)) 327.83/101.55
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.55
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.55
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.55
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.55
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.55
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.55
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.55
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.55
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.55
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.55
proper(terms(z0)) → terms(proper(z0)) 327.83/101.55
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.55
proper(recip(z0)) → recip(proper(z0)) 327.83/101.55
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.55
proper(s(z0)) → s(proper(z0)) 327.83/101.55
proper(0) → ok(0) 327.83/101.55
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.55
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.55
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.55
proper(nil) → ok(nil) 327.83/101.55
s(ok(z0)) → ok(s(z0)) 327.83/101.55
top(mark(z0)) → top(proper(z0)) 327.83/101.55
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.55
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.55
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.55
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.55
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.55
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.55
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.55
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.55
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.55
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.55
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.55
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.55
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.55
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.55
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.55
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.55
S(ok(z0)) → c44(S(z0))

S tuples:

SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.55
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1))

K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.55
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.55
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.55
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.55
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.55
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.55
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.55
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.55
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.55
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.55
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.55
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.55
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.55
S(ok(z0)) → c44(S(z0)) 327.83/101.55
SQR(mark(z0)) → c24(SQR(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.55

(91) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

SQR(ok(z0)) → c25(SQR(z0))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.55
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.55
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.55
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.55
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.55
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.55
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.55
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.55
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.55
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.55
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.55
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.55
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.55
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.55
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.55
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.55
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.55

POL(ADD(x₁, x₂)) = 0 327.83/101.55
POL(CONS(x₁, x₂)) = [3]x₁ + [3]x₂ 327.83/101.55
POL(DBL(x₁)) = [3]x₁ 327.83/101.55
POL(FIRST(x₁, x₂)) = [3]x₁ + [5]x₂ 327.83/101.55
POL(RECIP(x₁)) = [3]x₁ 327.83/101.55
POL(S(x₁)) = [5]x₁ 327.83/101.55
POL(SQR(x₁)) = [2]x₁ 327.83/101.55
POL(TERMS(x₁)) = [3]x₁ 327.83/101.55
POL(c18(x₁)) = x₁ 327.83/101.55
POL(c19(x₁)) = x₁ 327.83/101.55
POL(c20(x₁)) = x₁ 327.83/101.55
POL(c21(x₁)) = x₁ 327.83/101.55
POL(c22(x₁)) = x₁ 327.83/101.55
POL(c23(x₁)) = x₁ 327.83/101.55
POL(c24(x₁)) = x₁ 327.83/101.55
POL(c25(x₁)) = x₁ 327.83/101.55
POL(c26(x₁)) = x₁ 327.83/101.55
POL(c27(x₁)) = x₁ 327.83/101.55
POL(c28(x₁)) = x₁ 327.83/101.55
POL(c29(x₁)) = x₁ 327.83/101.55
POL(c30(x₁)) = x₁ 327.83/101.55
POL(c31(x₁)) = x₁ 327.83/101.55
POL(c32(x₁)) = x₁ 327.83/101.55
POL(c33(x₁)) = x₁ 327.83/101.55
POL(c44(x₁)) = x₁ 327.83/101.55
POL(mark(x₁)) = x₁ 327.83/101.55
POL(ok(x₁)) = [1] + x₁

327.83/101.55

(92) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.55
active(sqr(0)) → mark(0) 327.83/101.55
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.55
active(dbl(0)) → mark(0) 327.83/101.55
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.55
active(add(0, z0)) → mark(z0) 327.83/101.55
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.55
active(first(0, z0)) → mark(nil) 327.83/101.55
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.55
active(terms(z0)) → terms(active(z0)) 327.83/101.55
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.55
active(recip(z0)) → recip(active(z0)) 327.83/101.55
active(sqr(z0)) → sqr(active(z0)) 327.83/101.55
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.55
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.55
active(dbl(z0)) → dbl(active(z0)) 327.83/101.55
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.55
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.55
terms(mark(z0)) → mark(terms(z0)) 327.83/101.55
terms(ok(z0)) → ok(terms(z0)) 327.83/101.55
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.55
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.55
recip(mark(z0)) → mark(recip(z0)) 327.83/101.55
recip(ok(z0)) → ok(recip(z0)) 327.83/101.55
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.55
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.55
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.55
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.55
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.55
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.55
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.55
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.55
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.55
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.55
proper(terms(z0)) → terms(proper(z0)) 327.83/101.55
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.55
proper(recip(z0)) → recip(proper(z0)) 327.83/101.55
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.55
proper(s(z0)) → s(proper(z0)) 327.83/101.55
proper(0) → ok(0) 327.83/101.55
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.55
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.55
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.55
proper(nil) → ok(nil) 327.83/101.55
s(ok(z0)) → ok(s(z0)) 327.83/101.55
top(mark(z0)) → top(proper(z0)) 327.83/101.55
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.55
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.55
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.55
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.55
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.55
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.55
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.55
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.55
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.55
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.55
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.55
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.55
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.55
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.55
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.55
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.55
S(ok(z0)) → c44(S(z0))

S tuples:

ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1))

K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.55
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.55
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.55
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.55
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.55
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.55
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.55
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.55
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.55
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.55
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.55
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.55
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.55
S(ok(z0)) → c44(S(z0)) 327.83/101.55
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.55
SQR(ok(z0)) → c25(SQR(z0))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.55

(93) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))) transformation)

Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.

ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1))

We considered the (Usable) Rules:none
And the Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.55
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.55
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.55
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.55
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.55
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.55
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.55
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.55
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.55
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.55
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.55
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.55
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.55
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.55
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.55
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.55
S(ok(z0)) → c44(S(z0))

The order we found is given by the following interpretation:
Polynomial interpretation : 327.83/101.55

POL(ADD(x₁, x₂)) = [2]x₁ 327.83/101.55
POL(CONS(x₁, x₂)) = [5]x₁ + [5]x₂ 327.83/101.55
POL(DBL(x₁)) = [5]x₁ 327.83/101.55
POL(FIRST(x₁, x₂)) = [5]x₁ + [3]x₂ 327.83/101.55
POL(RECIP(x₁)) = [5]x₁ 327.83/101.55
POL(S(x₁)) = [5]x₁ 327.83/101.55
POL(SQR(x₁)) = [3]x₁ 327.83/101.55
POL(TERMS(x₁)) = [3]x₁ 327.83/101.55
POL(c18(x₁)) = x₁ 327.83/101.55
POL(c19(x₁)) = x₁ 327.83/101.55
POL(c20(x₁)) = x₁ 327.83/101.55
POL(c21(x₁)) = x₁ 327.83/101.55
POL(c22(x₁)) = x₁ 327.83/101.55
POL(c23(x₁)) = x₁ 327.83/101.55
POL(c24(x₁)) = x₁ 327.83/101.55
POL(c25(x₁)) = x₁ 327.83/101.55
POL(c26(x₁)) = x₁ 327.83/101.55
POL(c27(x₁)) = x₁ 327.83/101.55
POL(c28(x₁)) = x₁ 327.83/101.55
POL(c29(x₁)) = x₁ 327.83/101.55
POL(c30(x₁)) = x₁ 327.83/101.55
POL(c31(x₁)) = x₁ 327.83/101.55
POL(c32(x₁)) = x₁ 327.83/101.55
POL(c33(x₁)) = x₁ 327.83/101.55
POL(c44(x₁)) = x₁ 327.83/101.55
POL(mark(x₁)) = x₁ 327.83/101.55
POL(ok(x₁)) = [1] + x₁

327.83/101.55

(94) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 327.83/101.55
active(sqr(0)) → mark(0) 327.83/101.55
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 327.83/101.55
active(dbl(0)) → mark(0) 327.83/101.55
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 327.83/101.55
active(add(0, z0)) → mark(z0) 327.83/101.55
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 327.83/101.55
active(first(0, z0)) → mark(nil) 327.83/101.55
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 327.83/101.55
active(terms(z0)) → terms(active(z0)) 327.83/101.55
active(cons(z0, z1)) → cons(active(z0), z1) 327.83/101.55
active(recip(z0)) → recip(active(z0)) 327.83/101.55
active(sqr(z0)) → sqr(active(z0)) 327.83/101.55
active(add(z0, z1)) → add(active(z0), z1) 327.83/101.55
active(add(z0, z1)) → add(z0, active(z1)) 327.83/101.55
active(dbl(z0)) → dbl(active(z0)) 327.83/101.55
active(first(z0, z1)) → first(active(z0), z1) 327.83/101.55
active(first(z0, z1)) → first(z0, active(z1)) 327.83/101.55
terms(mark(z0)) → mark(terms(z0)) 327.83/101.55
terms(ok(z0)) → ok(terms(z0)) 327.83/101.55
cons(mark(z0), z1) → mark(cons(z0, z1)) 327.83/101.55
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 327.83/101.55
recip(mark(z0)) → mark(recip(z0)) 327.83/101.55
recip(ok(z0)) → ok(recip(z0)) 327.83/101.55
sqr(mark(z0)) → mark(sqr(z0)) 327.83/101.55
sqr(ok(z0)) → ok(sqr(z0)) 327.83/101.55
add(mark(z0), z1) → mark(add(z0, z1)) 327.83/101.55
add(z0, mark(z1)) → mark(add(z0, z1)) 327.83/101.55
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 327.83/101.55
dbl(mark(z0)) → mark(dbl(z0)) 327.83/101.55
dbl(ok(z0)) → ok(dbl(z0)) 327.83/101.55
first(mark(z0), z1) → mark(first(z0, z1)) 327.83/101.55
first(z0, mark(z1)) → mark(first(z0, z1)) 327.83/101.55
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 327.83/101.55
proper(terms(z0)) → terms(proper(z0)) 327.83/101.55
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 327.83/101.55
proper(recip(z0)) → recip(proper(z0)) 327.83/101.55
proper(sqr(z0)) → sqr(proper(z0)) 327.83/101.55
proper(s(z0)) → s(proper(z0)) 327.83/101.55
proper(0) → ok(0) 327.83/101.55
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 327.83/101.55
proper(dbl(z0)) → dbl(proper(z0)) 327.83/101.55
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 327.83/101.55
proper(nil) → ok(nil) 327.83/101.55
s(ok(z0)) → ok(s(z0)) 327.83/101.55
top(mark(z0)) → top(proper(z0)) 327.83/101.55
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.55
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.55
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.55
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.55
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.55
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.55
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.55
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.55
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.55
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.55
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1)) 327.83/101.55
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.55
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.55
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.55
FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.55
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.55
S(ok(z0)) → c44(S(z0))

S tuples:none
K tuples:

FIRST(z0, mark(z1)) → c32(FIRST(z0, z1)) 327.83/101.55
TERMS(mark(z0)) → c18(TERMS(z0)) 327.83/101.55
TERMS(ok(z0)) → c19(TERMS(z0)) 327.83/101.55
RECIP(mark(z0)) → c22(RECIP(z0)) 327.83/101.55
RECIP(ok(z0)) → c23(RECIP(z0)) 327.83/101.55
DBL(mark(z0)) → c29(DBL(z0)) 327.83/101.55
DBL(ok(z0)) → c30(DBL(z0)) 327.83/101.55
FIRST(mark(z0), z1) → c31(FIRST(z0, z1)) 327.83/101.55
FIRST(ok(z0), ok(z1)) → c33(FIRST(z0, z1)) 327.83/101.55
CONS(mark(z0), z1) → c20(CONS(z0, z1)) 327.83/101.55
CONS(ok(z0), ok(z1)) → c21(CONS(z0, z1)) 327.83/101.55
ADD(mark(z0), z1) → c26(ADD(z0, z1)) 327.83/101.55
ADD(z0, mark(z1)) → c27(ADD(z0, z1)) 327.83/101.55
S(ok(z0)) → c44(S(z0)) 327.83/101.55
SQR(mark(z0)) → c24(SQR(z0)) 327.83/101.55
SQR(ok(z0)) → c25(SQR(z0)) 327.83/101.55
ADD(ok(z0), ok(z1)) → c28(ADD(z0, z1))

Defined Rule Symbols:

active, terms, cons, recip, sqr, add, dbl, first, proper, s, top

Defined Pair Symbols:

TERMS, CONS, RECIP, SQR, ADD, DBL, FIRST, S

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c44

327.83/101.55

(95) SIsEmptyProof (BOTH BOUNDS(ID, ID) transformation)

The set S is empty

327.83/101.55

(96) BOUNDS(O(1), O(1))

327.83/101.55