330.87/103.43 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml

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330.87/103.43
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^2)).

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 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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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 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))

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↳16 CdtProblem

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

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↳18 CdtProblem

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↳19 CdtRhsSimplificationProcessorProof (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 CdtNarrowingProof (BOTH BOUNDS(ID, ID))

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↳26 CdtProblem

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

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↳28 CdtProblem

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

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↳30 CdtProblem

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

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↳32 CdtProblem

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

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↳34 CdtProblem

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

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↳36 CdtProblem

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

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↳38 CdtProblem

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

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↳40 CdtProblem

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

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↳42 CdtProblem

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

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↳44 CdtProblem

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

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↳46 CdtProblem

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

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↳48 CdtProblem

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

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↳50 CdtProblem

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

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↳52 CdtProblem

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

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↳54 CdtProblem

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

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↳56 CdtProblem

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

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↳58 CdtProblem

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

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↳60 CdtProblem

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

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↳62 CdtProblem

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↳63 CdtUnreachableProof (⇔)

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↳64 CdtProblem

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

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↳66 CdtProblem

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

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↳68 CdtProblem

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

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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^2))))

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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 SIsEmptyProof (BOTH BOUNDS(ID, ID))

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↳92 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)))) 331.23/103.55
active(sqr(0)) → mark(0) 331.23/103.55
active(sqr(s(X))) → mark(s(add(sqr(X), dbl(X)))) 331.23/103.55
active(dbl(0)) → mark(0) 331.23/103.55
active(dbl(s(X))) → mark(s(s(dbl(X)))) 331.23/103.55
active(add(0, X)) → mark(X) 331.23/103.55
active(add(s(X), Y)) → mark(s(add(X, Y))) 331.23/103.55
active(first(0, X)) → mark(nil) 331.23/103.55
active(first(s(X), cons(Y, Z))) → mark(cons(Y, first(X, Z))) 331.23/103.55
active(terms(X)) → terms(active(X)) 331.23/103.55
active(cons(X1, X2)) → cons(active(X1), X2) 331.23/103.55
active(recip(X)) → recip(active(X)) 331.23/103.55
active(sqr(X)) → sqr(active(X)) 331.23/103.55
active(s(X)) → s(active(X)) 331.23/103.55
active(add(X1, X2)) → add(active(X1), X2) 331.23/103.55
active(add(X1, X2)) → add(X1, active(X2)) 331.23/103.55
active(dbl(X)) → dbl(active(X)) 331.23/103.55
active(first(X1, X2)) → first(active(X1), X2) 331.23/103.55
active(first(X1, X2)) → first(X1, active(X2)) 331.23/103.55
terms(mark(X)) → mark(terms(X)) 331.23/103.55
cons(mark(X1), X2) → mark(cons(X1, X2)) 331.23/103.55
recip(mark(X)) → mark(recip(X)) 331.23/103.55
sqr(mark(X)) → mark(sqr(X)) 331.23/103.55
s(mark(X)) → mark(s(X)) 331.23/103.55
add(mark(X1), X2) → mark(add(X1, X2)) 331.23/103.55
add(X1, mark(X2)) → mark(add(X1, X2)) 331.23/103.55
dbl(mark(X)) → mark(dbl(X)) 331.23/103.55
first(mark(X1), X2) → mark(first(X1, X2)) 331.23/103.55
first(X1, mark(X2)) → mark(first(X1, X2)) 331.23/103.55
proper(terms(X)) → terms(proper(X)) 331.23/103.55
proper(cons(X1, X2)) → cons(proper(X1), proper(X2)) 331.23/103.55
proper(recip(X)) → recip(proper(X)) 331.23/103.55
proper(sqr(X)) → sqr(proper(X)) 331.23/103.55
proper(s(X)) → s(proper(X)) 331.23/103.55
proper(0) → ok(0) 331.23/103.55
proper(add(X1, X2)) → add(proper(X1), proper(X2)) 331.23/103.55
proper(dbl(X)) → dbl(proper(X)) 331.23/103.55
proper(first(X1, X2)) → first(proper(X1), proper(X2)) 331.23/103.55
proper(nil) → ok(nil) 331.23/103.55
terms(ok(X)) → ok(terms(X)) 331.23/103.55
cons(ok(X1), ok(X2)) → ok(cons(X1, X2)) 331.23/103.55
recip(ok(X)) → ok(recip(X)) 331.23/103.55
sqr(ok(X)) → ok(sqr(X)) 331.23/103.55
s(ok(X)) → ok(s(X)) 331.23/103.55
add(ok(X1), ok(X2)) → ok(add(X1, X2)) 331.23/103.55
dbl(ok(X)) → ok(dbl(X)) 331.23/103.55
first(ok(X1), ok(X2)) → ok(first(X1, X2)) 331.23/103.55
top(mark(X)) → top(proper(X)) 331.23/103.55
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)))) 331.23/103.55
active(sqr(0)) → mark(0) 331.23/103.55
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 331.23/103.55
active(dbl(0)) → mark(0) 331.23/103.55
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 331.23/103.55
active(add(0, z0)) → mark(z0) 331.23/103.55
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 331.23/103.55
active(first(0, z0)) → mark(nil) 331.23/103.55
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 331.23/103.55
active(terms(z0)) → terms(active(z0)) 331.23/103.55
active(cons(z0, z1)) → cons(active(z0), z1) 331.23/103.55
active(recip(z0)) → recip(active(z0)) 331.23/103.55
active(sqr(z0)) → sqr(active(z0)) 331.23/103.55
active(s(z0)) → s(active(z0)) 331.23/103.55
active(add(z0, z1)) → add(active(z0), z1) 331.23/103.55
active(add(z0, z1)) → add(z0, active(z1)) 331.23/103.55
active(dbl(z0)) → dbl(active(z0)) 331.23/103.55
active(first(z0, z1)) → first(active(z0), z1) 331.23/103.55
active(first(z0, z1)) → first(z0, active(z1)) 331.23/103.55
terms(mark(z0)) → mark(terms(z0)) 331.23/103.55
terms(ok(z0)) → ok(terms(z0)) 331.23/103.55
cons(mark(z0), z1) → mark(cons(z0, z1)) 331.23/103.55
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 331.23/103.55
recip(mark(z0)) → mark(recip(z0)) 331.23/103.55
recip(ok(z0)) → ok(recip(z0)) 331.23/103.55
sqr(mark(z0)) → mark(sqr(z0)) 331.23/103.55
sqr(ok(z0)) → ok(sqr(z0)) 331.23/103.55
s(mark(z0)) → mark(s(z0)) 331.23/103.55
s(ok(z0)) → ok(s(z0)) 331.23/103.55
add(mark(z0), z1) → mark(add(z0, z1)) 331.23/103.55
add(z0, mark(z1)) → mark(add(z0, z1)) 331.23/103.55
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 331.23/103.55
dbl(mark(z0)) → mark(dbl(z0)) 331.23/103.55
dbl(ok(z0)) → ok(dbl(z0)) 331.23/103.55
first(mark(z0), z1) → mark(first(z0, z1)) 331.23/103.55
first(z0, mark(z1)) → mark(first(z0, z1)) 331.23/103.55
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 331.23/103.55
proper(terms(z0)) → terms(proper(z0)) 331.23/103.55
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 331.23/103.55
proper(recip(z0)) → recip(proper(z0)) 331.23/103.55
proper(sqr(z0)) → sqr(proper(z0)) 331.23/103.55
proper(s(z0)) → s(proper(z0)) 331.23/103.55
proper(0) → ok(0) 331.23/103.55
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 331.23/103.55
proper(dbl(z0)) → dbl(proper(z0)) 331.23/103.55
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 331.23/103.55
proper(nil) → ok(nil) 331.23/103.55
top(mark(z0)) → top(proper(z0)) 331.23/103.55
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)) 331.23/103.55
ACTIVE(sqr(s(z0))) → c2(S(add(sqr(z0), dbl(z0))), ADD(sqr(z0), dbl(z0)), SQR(z0), DBL(z0)) 331.23/103.55
ACTIVE(dbl(s(z0))) → c4(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 331.23/103.55
ACTIVE(add(s(z0), z1)) → c6(S(add(z0, z1)), ADD(z0, z1)) 331.23/103.55
ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2)) 331.23/103.55
ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 331.23/103.55
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 331.23/103.55
TERMS(mark(z0)) → c19(TERMS(z0)) 331.23/103.55
TERMS(ok(z0)) → c20(TERMS(z0)) 331.23/103.55
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 331.23/103.55
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 331.23/103.55
RECIP(mark(z0)) → c23(RECIP(z0)) 331.23/103.55
RECIP(ok(z0)) → c24(RECIP(z0)) 331.23/103.55
SQR(mark(z0)) → c25(SQR(z0)) 331.23/103.55
SQR(ok(z0)) → c26(SQR(z0)) 331.23/103.55
S(mark(z0)) → c27(S(z0)) 331.23/103.55
S(ok(z0)) → c28(S(z0)) 331.23/103.55
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 331.23/103.55
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 331.23/103.55
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 331.23/103.55
DBL(mark(z0)) → c32(DBL(z0)) 331.23/103.55
DBL(ok(z0)) → c33(DBL(z0)) 331.23/103.55
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 331.23/103.55
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 331.23/103.55
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 331.23/103.55
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.23/103.55
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.23/103.55
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.23/103.55
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 331.23/103.55
TOP(ok(z0)) → c48(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)) 331.23/103.55
ACTIVE(sqr(s(z0))) → c2(S(add(sqr(z0), dbl(z0))), ADD(sqr(z0), dbl(z0)), SQR(z0), DBL(z0)) 331.23/103.55
ACTIVE(dbl(s(z0))) → c4(S(s(dbl(z0))), S(dbl(z0)), DBL(z0)) 331.23/103.55
ACTIVE(add(s(z0), z1)) → c6(S(add(z0, z1)), ADD(z0, z1)) 331.23/103.55
ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2)) 331.23/103.55
ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 331.23/103.55
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 331.23/103.55
TERMS(mark(z0)) → c19(TERMS(z0)) 331.23/103.55
TERMS(ok(z0)) → c20(TERMS(z0)) 331.23/103.55
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 331.23/103.55
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 331.23/103.55
RECIP(mark(z0)) → c23(RECIP(z0)) 331.23/103.55
RECIP(ok(z0)) → c24(RECIP(z0)) 331.23/103.55
SQR(mark(z0)) → c25(SQR(z0)) 331.23/103.55
SQR(ok(z0)) → c26(SQR(z0)) 331.23/103.55
S(mark(z0)) → c27(S(z0)) 331.23/103.55
S(ok(z0)) → c28(S(z0)) 331.23/103.55
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 331.23/103.55
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 331.23/103.55
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 331.23/103.55
DBL(mark(z0)) → c32(DBL(z0)) 331.23/103.55
DBL(ok(z0)) → c33(DBL(z0)) 331.23/103.55
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 331.23/103.55
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 331.23/103.55
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 331.23/103.55
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.23/103.55
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.23/103.55
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.23/103.55
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 331.23/103.55
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, PROPER, 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, c39, c40, c41, c43, c44, c45, c47, c48

331.23/103.55

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

Removed 8 trailing tuple parts

331.23/103.55

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 331.23/103.55
active(sqr(0)) → mark(0) 331.23/103.55
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 331.23/103.55
active(dbl(0)) → mark(0) 331.23/103.55
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 331.23/103.55
active(add(0, z0)) → mark(z0) 331.23/103.55
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 331.23/103.55
active(first(0, z0)) → mark(nil) 331.23/103.55
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 331.23/103.55
active(terms(z0)) → terms(active(z0)) 331.23/103.55
active(cons(z0, z1)) → cons(active(z0), z1) 331.23/103.55
active(recip(z0)) → recip(active(z0)) 331.23/103.55
active(sqr(z0)) → sqr(active(z0)) 331.23/103.55
active(s(z0)) → s(active(z0)) 331.23/103.55
active(add(z0, z1)) → add(active(z0), z1) 331.23/103.55
active(add(z0, z1)) → add(z0, active(z1)) 331.23/103.55
active(dbl(z0)) → dbl(active(z0)) 331.23/103.55
active(first(z0, z1)) → first(active(z0), z1) 331.23/103.55
active(first(z0, z1)) → first(z0, active(z1)) 331.23/103.55
terms(mark(z0)) → mark(terms(z0)) 331.23/103.55
terms(ok(z0)) → ok(terms(z0)) 331.23/103.55
cons(mark(z0), z1) → mark(cons(z0, z1)) 331.23/103.55
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 331.23/103.55
recip(mark(z0)) → mark(recip(z0)) 331.23/103.55
recip(ok(z0)) → ok(recip(z0)) 331.23/103.55
sqr(mark(z0)) → mark(sqr(z0)) 331.23/103.55
sqr(ok(z0)) → ok(sqr(z0)) 331.23/103.55
s(mark(z0)) → mark(s(z0)) 331.23/103.55
s(ok(z0)) → ok(s(z0)) 331.23/103.55
add(mark(z0), z1) → mark(add(z0, z1)) 331.23/103.55
add(z0, mark(z1)) → mark(add(z0, z1)) 331.23/103.55
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 331.23/103.55
dbl(mark(z0)) → mark(dbl(z0)) 331.23/103.55
dbl(ok(z0)) → ok(dbl(z0)) 331.23/103.55
first(mark(z0), z1) → mark(first(z0, z1)) 331.23/103.55
first(z0, mark(z1)) → mark(first(z0, z1)) 331.23/103.55
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 331.23/103.55
proper(terms(z0)) → terms(proper(z0)) 331.23/103.55
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 331.23/103.55
proper(recip(z0)) → recip(proper(z0)) 331.23/103.55
proper(sqr(z0)) → sqr(proper(z0)) 331.23/103.55
proper(s(z0)) → s(proper(z0)) 331.23/103.55
proper(0) → ok(0) 331.23/103.55
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 331.23/103.55
proper(dbl(z0)) → dbl(proper(z0)) 331.23/103.55
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 331.23/103.55
proper(nil) → ok(nil) 331.23/103.55
top(mark(z0)) → top(proper(z0)) 331.23/103.55
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2)) 331.23/103.55
ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 331.23/103.55
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 331.23/103.55
TERMS(mark(z0)) → c19(TERMS(z0)) 331.23/103.55
TERMS(ok(z0)) → c20(TERMS(z0)) 331.23/103.55
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 331.23/103.55
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 331.23/103.55
RECIP(mark(z0)) → c23(RECIP(z0)) 331.23/103.55
RECIP(ok(z0)) → c24(RECIP(z0)) 331.23/103.55
SQR(mark(z0)) → c25(SQR(z0)) 331.23/103.55
SQR(ok(z0)) → c26(SQR(z0)) 331.23/103.55
S(mark(z0)) → c27(S(z0)) 331.23/103.55
S(ok(z0)) → c28(S(z0)) 331.23/103.55
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 331.23/103.55
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 331.23/103.55
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 331.23/103.55
DBL(mark(z0)) → c32(DBL(z0)) 331.23/103.55
DBL(ok(z0)) → c33(DBL(z0)) 331.23/103.55
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 331.23/103.55
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 331.23/103.55
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 331.23/103.55
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.23/103.55
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.23/103.55
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 331.23/103.55
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.23/103.55
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 331.23/103.55
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(terms(z0)) → c(SQR(z0), S(z0)) 331.23/103.55
ACTIVE(sqr(s(z0))) → c2(SQR(z0), DBL(z0)) 331.23/103.55
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 331.23/103.55
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))

S tuples:

ACTIVE(first(s(z0), cons(z1, z2))) → c8(CONS(z1, first(z0, z2)), FIRST(z0, z2)) 331.23/103.55
ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 331.23/103.55
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 331.23/103.55
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 331.23/103.55
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 331.23/103.55
TERMS(mark(z0)) → c19(TERMS(z0)) 331.23/103.55
TERMS(ok(z0)) → c20(TERMS(z0)) 331.23/103.55
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 331.60/103.65
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 331.60/103.65
RECIP(mark(z0)) → c23(RECIP(z0)) 331.60/103.65
RECIP(ok(z0)) → c24(RECIP(z0)) 331.60/103.65
SQR(mark(z0)) → c25(SQR(z0)) 331.60/103.65
SQR(ok(z0)) → c26(SQR(z0)) 331.60/103.65
S(mark(z0)) → c27(S(z0)) 331.60/103.65
S(ok(z0)) → c28(S(z0)) 331.60/103.65
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 331.60/103.65
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 331.60/103.65
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 331.60/103.65
DBL(mark(z0)) → c32(DBL(z0)) 331.60/103.65
DBL(ok(z0)) → c33(DBL(z0)) 331.60/103.65
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 331.60/103.65
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 331.60/103.65
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 331.60/103.65
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 331.60/103.65
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(terms(z0)) → c(SQR(z0), S(z0)) 331.60/103.65
ACTIVE(sqr(s(z0))) → c2(SQR(z0), DBL(z0)) 331.60/103.65
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 331.60/103.65
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

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, c39, c40, c41, c43, c44, c45, c47, c48, c, c2, c4, c6

331.60/103.65

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

Split RHS of tuples not part of any SCC

331.60/103.65

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 331.60/103.65
active(sqr(0)) → mark(0) 331.60/103.65
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 331.60/103.65
active(dbl(0)) → mark(0) 331.60/103.65
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 331.60/103.65
active(add(0, z0)) → mark(z0) 331.60/103.65
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 331.60/103.65
active(first(0, z0)) → mark(nil) 331.60/103.65
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 331.60/103.65
active(terms(z0)) → terms(active(z0)) 331.60/103.65
active(cons(z0, z1)) → cons(active(z0), z1) 331.60/103.65
active(recip(z0)) → recip(active(z0)) 331.60/103.65
active(sqr(z0)) → sqr(active(z0)) 331.60/103.65
active(s(z0)) → s(active(z0)) 331.60/103.65
active(add(z0, z1)) → add(active(z0), z1) 331.60/103.65
active(add(z0, z1)) → add(z0, active(z1)) 331.60/103.65
active(dbl(z0)) → dbl(active(z0)) 331.60/103.65
active(first(z0, z1)) → first(active(z0), z1) 331.60/103.65
active(first(z0, z1)) → first(z0, active(z1)) 331.60/103.65
terms(mark(z0)) → mark(terms(z0)) 331.60/103.65
terms(ok(z0)) → ok(terms(z0)) 331.60/103.65
cons(mark(z0), z1) → mark(cons(z0, z1)) 331.60/103.65
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 331.60/103.65
recip(mark(z0)) → mark(recip(z0)) 331.60/103.65
recip(ok(z0)) → ok(recip(z0)) 331.60/103.65
sqr(mark(z0)) → mark(sqr(z0)) 331.60/103.65
sqr(ok(z0)) → ok(sqr(z0)) 331.60/103.65
s(mark(z0)) → mark(s(z0)) 331.60/103.65
s(ok(z0)) → ok(s(z0)) 331.60/103.65
add(mark(z0), z1) → mark(add(z0, z1)) 331.60/103.65
add(z0, mark(z1)) → mark(add(z0, z1)) 331.60/103.65
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 331.60/103.65
dbl(mark(z0)) → mark(dbl(z0)) 331.60/103.65
dbl(ok(z0)) → ok(dbl(z0)) 331.60/103.65
first(mark(z0), z1) → mark(first(z0, z1)) 331.60/103.65
first(z0, mark(z1)) → mark(first(z0, z1)) 331.60/103.65
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 331.60/103.65
proper(terms(z0)) → terms(proper(z0)) 331.60/103.65
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 331.60/103.65
proper(recip(z0)) → recip(proper(z0)) 331.60/103.65
proper(sqr(z0)) → sqr(proper(z0)) 331.60/103.65
proper(s(z0)) → s(proper(z0)) 331.60/103.65
proper(0) → ok(0) 331.60/103.65
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 331.60/103.65
proper(dbl(z0)) → dbl(proper(z0)) 331.60/103.65
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 331.60/103.65
proper(nil) → ok(nil) 331.60/103.65
top(mark(z0)) → top(proper(z0)) 331.60/103.65
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 331.60/103.65
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 331.60/103.65
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 331.60/103.65
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 331.60/103.65
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 331.60/103.65
TERMS(mark(z0)) → c19(TERMS(z0)) 331.60/103.65
TERMS(ok(z0)) → c20(TERMS(z0)) 331.60/103.65
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 331.60/103.65
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 331.60/103.65
RECIP(mark(z0)) → c23(RECIP(z0)) 331.60/103.65
RECIP(ok(z0)) → c24(RECIP(z0)) 331.60/103.65
SQR(mark(z0)) → c25(SQR(z0)) 331.60/103.65
SQR(ok(z0)) → c26(SQR(z0)) 331.60/103.65
S(mark(z0)) → c27(S(z0)) 331.60/103.65
S(ok(z0)) → c28(S(z0)) 331.60/103.65
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 331.60/103.65
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 331.60/103.65
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 331.60/103.65
DBL(mark(z0)) → c32(DBL(z0)) 331.60/103.65
DBL(ok(z0)) → c33(DBL(z0)) 331.60/103.65
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 331.60/103.65
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 331.60/103.65
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 331.60/103.65
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 331.60/103.65
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 331.60/103.65
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 331.60/103.65
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 331.60/103.65
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 331.60/103.65
ACTIVE(terms(z0)) → c1(SQR(z0)) 331.60/103.65
ACTIVE(terms(z0)) → c1(S(z0)) 331.60/103.65
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 331.60/103.65
ACTIVE(sqr(s(z0))) → c1(DBL(z0))

S tuples:

ACTIVE(terms(z0)) → c9(TERMS(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 331.60/103.65
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 331.60/103.65
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 331.60/103.65
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 331.60/103.65
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 331.60/103.65
TERMS(mark(z0)) → c19(TERMS(z0)) 331.60/103.65
TERMS(ok(z0)) → c20(TERMS(z0)) 331.60/103.65
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 331.60/103.65
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 331.60/103.65
RECIP(mark(z0)) → c23(RECIP(z0)) 331.60/103.65
RECIP(ok(z0)) → c24(RECIP(z0)) 331.60/103.65
SQR(mark(z0)) → c25(SQR(z0)) 331.60/103.65
SQR(ok(z0)) → c26(SQR(z0)) 331.60/103.65
S(mark(z0)) → c27(S(z0)) 331.60/103.65
S(ok(z0)) → c28(S(z0)) 331.60/103.65
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 331.60/103.65
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 331.60/103.65
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 331.60/103.65
DBL(mark(z0)) → c32(DBL(z0)) 331.60/103.65
DBL(ok(z0)) → c33(DBL(z0)) 331.60/103.65
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 331.60/103.65
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 331.60/103.65
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 331.60/103.65
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 331.60/103.65
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 331.60/103.65
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 331.60/103.65
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 331.60/103.65
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 331.60/103.65
ACTIVE(terms(z0)) → c1(SQR(z0)) 331.60/103.65
ACTIVE(terms(z0)) → c1(S(z0)) 331.60/103.65
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 331.60/103.65
ACTIVE(sqr(s(z0))) → c1(DBL(z0))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, PROPER, 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, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1

331.60/103.65

(7) 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))) 331.60/103.65
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 331.60/103.65
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 331.60/103.65
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 331.60/103.65
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 331.60/103.65
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 331.60/103.65
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 331.60/103.65
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 331.60/103.65
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 331.60/103.65
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 331.60/103.65
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 331.60/103.65
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 331.60/103.65
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 331.60/103.65
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 331.60/103.65
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 331.60/103.65
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 331.60/103.65
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 331.60/103.65
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 331.60/103.65
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))

331.60/103.65

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 331.60/103.65
active(sqr(0)) → mark(0) 331.60/103.65
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 331.60/103.65
active(dbl(0)) → mark(0) 331.60/103.65
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 331.60/103.65
active(add(0, z0)) → mark(z0) 331.60/103.65
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 331.60/103.65
active(first(0, z0)) → mark(nil) 331.60/103.65
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 331.60/103.65
active(terms(z0)) → terms(active(z0)) 331.60/103.65
active(cons(z0, z1)) → cons(active(z0), z1) 331.60/103.65
active(recip(z0)) → recip(active(z0)) 331.60/103.65
active(sqr(z0)) → sqr(active(z0)) 331.60/103.65
active(s(z0)) → s(active(z0)) 331.60/103.65
active(add(z0, z1)) → add(active(z0), z1) 331.60/103.65
active(add(z0, z1)) → add(z0, active(z1)) 331.60/103.65
active(dbl(z0)) → dbl(active(z0)) 331.60/103.65
active(first(z0, z1)) → first(active(z0), z1) 331.60/103.65
active(first(z0, z1)) → first(z0, active(z1)) 331.60/103.65
terms(mark(z0)) → mark(terms(z0)) 331.60/103.65
terms(ok(z0)) → ok(terms(z0)) 331.60/103.65
cons(mark(z0), z1) → mark(cons(z0, z1)) 331.60/103.65
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 331.60/103.65
recip(mark(z0)) → mark(recip(z0)) 331.60/103.65
recip(ok(z0)) → ok(recip(z0)) 331.60/103.65
sqr(mark(z0)) → mark(sqr(z0)) 331.60/103.65
sqr(ok(z0)) → ok(sqr(z0)) 331.60/103.65
s(mark(z0)) → mark(s(z0)) 331.60/103.65
s(ok(z0)) → ok(s(z0)) 331.60/103.65
add(mark(z0), z1) → mark(add(z0, z1)) 331.60/103.65
add(z0, mark(z1)) → mark(add(z0, z1)) 331.60/103.65
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 331.60/103.65
dbl(mark(z0)) → mark(dbl(z0)) 331.60/103.65
dbl(ok(z0)) → ok(dbl(z0)) 331.60/103.65
first(mark(z0), z1) → mark(first(z0, z1)) 331.60/103.65
first(z0, mark(z1)) → mark(first(z0, z1)) 331.60/103.65
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 331.60/103.65
proper(terms(z0)) → terms(proper(z0)) 331.60/103.65
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 331.60/103.65
proper(recip(z0)) → recip(proper(z0)) 331.60/103.65
proper(sqr(z0)) → sqr(proper(z0)) 331.60/103.65
proper(s(z0)) → s(proper(z0)) 331.60/103.65
proper(0) → ok(0) 331.60/103.65
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 331.60/103.65
proper(dbl(z0)) → dbl(proper(z0)) 331.60/103.65
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 331.60/103.65
proper(nil) → ok(nil) 331.60/103.65
top(mark(z0)) → top(proper(z0)) 331.60/103.65
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(cons(z0, z1)) → c10(CONS(active(z0), z1), ACTIVE(z0)) 331.60/103.65
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 331.60/103.65
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 331.60/103.65
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 331.60/103.65
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 331.60/103.65
TERMS(mark(z0)) → c19(TERMS(z0)) 331.60/103.65
TERMS(ok(z0)) → c20(TERMS(z0)) 331.60/103.65
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 331.60/103.65
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 331.60/103.65
RECIP(mark(z0)) → c23(RECIP(z0)) 331.60/103.65
RECIP(ok(z0)) → c24(RECIP(z0)) 331.60/103.65
SQR(mark(z0)) → c25(SQR(z0)) 331.60/103.65
SQR(ok(z0)) → c26(SQR(z0)) 331.60/103.65
S(mark(z0)) → c27(S(z0)) 331.60/103.65
S(ok(z0)) → c28(S(z0)) 331.60/103.65
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 331.60/103.65
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 331.60/103.65
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 331.60/103.65
DBL(mark(z0)) → c32(DBL(z0)) 331.60/103.65
DBL(ok(z0)) → c33(DBL(z0)) 331.60/103.65
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 331.60/103.65
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 331.60/103.65
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 331.60/103.65
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 331.60/103.65
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 331.60/103.65
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 331.60/103.65
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 331.60/103.65
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 331.60/103.65
ACTIVE(terms(z0)) → c1(SQR(z0)) 331.60/103.65
ACTIVE(terms(z0)) → c1(S(z0)) 331.60/103.65
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 331.60/103.65
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 331.60/103.65
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 331.60/103.65
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 331.60/103.65
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 331.60/103.65
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 331.60/103.65
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 331.60/103.65
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 331.60/103.65
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 331.60/103.65
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 331.60/103.65
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 331.60/103.65
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 331.60/103.65
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 331.60/103.65
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 331.60/103.65
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 331.60/103.65
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 331.60/103.65
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 331.60/103.65
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 331.60/103.65
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 331.60/103.65
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 331.60/103.65
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)) 331.60/103.65
ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 331.60/103.65
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 331.60/103.65
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 331.60/103.65
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 331.60/103.65
TERMS(mark(z0)) → c19(TERMS(z0)) 331.60/103.65
TERMS(ok(z0)) → c20(TERMS(z0)) 331.60/103.65
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 331.60/103.65
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 331.60/103.65
RECIP(mark(z0)) → c23(RECIP(z0)) 331.60/103.65
RECIP(ok(z0)) → c24(RECIP(z0)) 331.60/103.65
SQR(mark(z0)) → c25(SQR(z0)) 331.60/103.65
SQR(ok(z0)) → c26(SQR(z0)) 331.60/103.65
S(mark(z0)) → c27(S(z0)) 331.60/103.65
S(ok(z0)) → c28(S(z0)) 331.60/103.65
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 331.60/103.65
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 331.60/103.65
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 331.60/103.65
DBL(mark(z0)) → c32(DBL(z0)) 331.60/103.65
DBL(ok(z0)) → c33(DBL(z0)) 331.60/103.65
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 331.60/103.65
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 331.60/103.65
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 331.60/103.65
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 331.60/103.65
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 331.60/103.65
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 331.60/103.65
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 331.60/103.65
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 331.60/103.65
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 331.60/103.65
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 331.60/103.65
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 331.60/103.65
ACTIVE(terms(z0)) → c1(SQR(z0)) 331.60/103.65
ACTIVE(terms(z0)) → c1(S(z0)) 331.60/103.65
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 331.60/103.65
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 331.60/103.65
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 331.60/103.65
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 331.60/103.65
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 331.60/103.65
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 331.60/103.65
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 331.60/103.65
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 331.60/103.65
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 331.60/103.65
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 331.60/103.65
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 331.60/103.65
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 331.60/103.65
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 331.60/103.65
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 331.60/103.65
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 331.60/103.65
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 331.60/103.65
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 331.60/103.65
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 331.60/103.65
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.60/104.18
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.60/104.18
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9

333.60/104.18

(9) 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))) 333.60/104.18
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 333.60/104.18
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.60/104.18
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.60/104.18
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.60/104.18
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.60/104.18
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.60/104.18
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.60/104.18
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)))) 333.60/104.18
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.60/104.18
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.60/104.18
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.60/104.18
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.60/104.18
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.60/104.18
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.60/104.18
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.60/104.18
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.60/104.18
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.60/104.18
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))

333.60/104.18

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 333.60/104.18
active(sqr(0)) → mark(0) 333.60/104.18
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 333.60/104.18
active(dbl(0)) → mark(0) 333.60/104.18
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 333.60/104.18
active(add(0, z0)) → mark(z0) 333.60/104.18
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 333.60/104.18
active(first(0, z0)) → mark(nil) 333.60/104.18
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 333.60/104.18
active(terms(z0)) → terms(active(z0)) 333.60/104.18
active(cons(z0, z1)) → cons(active(z0), z1) 333.60/104.18
active(recip(z0)) → recip(active(z0)) 333.60/104.18
active(sqr(z0)) → sqr(active(z0)) 333.60/104.18
active(s(z0)) → s(active(z0)) 333.60/104.18
active(add(z0, z1)) → add(active(z0), z1) 333.60/104.18
active(add(z0, z1)) → add(z0, active(z1)) 333.60/104.18
active(dbl(z0)) → dbl(active(z0)) 333.60/104.18
active(first(z0, z1)) → first(active(z0), z1) 333.60/104.18
active(first(z0, z1)) → first(z0, active(z1)) 333.60/104.18
terms(mark(z0)) → mark(terms(z0)) 333.60/104.18
terms(ok(z0)) → ok(terms(z0)) 333.60/104.18
cons(mark(z0), z1) → mark(cons(z0, z1)) 333.60/104.18
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 333.60/104.18
recip(mark(z0)) → mark(recip(z0)) 333.60/104.18
recip(ok(z0)) → ok(recip(z0)) 333.60/104.18
sqr(mark(z0)) → mark(sqr(z0)) 333.60/104.18
sqr(ok(z0)) → ok(sqr(z0)) 333.60/104.18
s(mark(z0)) → mark(s(z0)) 333.60/104.18
s(ok(z0)) → ok(s(z0)) 333.60/104.18
add(mark(z0), z1) → mark(add(z0, z1)) 333.60/104.18
add(z0, mark(z1)) → mark(add(z0, z1)) 333.60/104.18
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 333.60/104.18
dbl(mark(z0)) → mark(dbl(z0)) 333.60/104.18
dbl(ok(z0)) → ok(dbl(z0)) 333.60/104.18
first(mark(z0), z1) → mark(first(z0, z1)) 333.60/104.18
first(z0, mark(z1)) → mark(first(z0, z1)) 333.60/104.18
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 333.60/104.18
proper(terms(z0)) → terms(proper(z0)) 333.60/104.18
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 333.60/104.18
proper(recip(z0)) → recip(proper(z0)) 333.60/104.18
proper(sqr(z0)) → sqr(proper(z0)) 333.60/104.18
proper(s(z0)) → s(proper(z0)) 333.60/104.18
proper(0) → ok(0) 333.60/104.18
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 333.60/104.18
proper(dbl(z0)) → dbl(proper(z0)) 333.60/104.18
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 333.60/104.18
proper(nil) → ok(nil) 333.60/104.18
top(mark(z0)) → top(proper(z0)) 333.60/104.18
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(recip(z0)) → c11(RECIP(active(z0)), ACTIVE(z0)) 333.60/104.18
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 333.60/104.18
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 333.60/104.18
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.60/104.18
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.60/104.18
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.60/104.18
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.60/104.18
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.60/104.18
TERMS(mark(z0)) → c19(TERMS(z0)) 333.60/104.18
TERMS(ok(z0)) → c20(TERMS(z0)) 333.60/104.18
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.60/104.18
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.60/104.18
RECIP(mark(z0)) → c23(RECIP(z0)) 333.60/104.18
RECIP(ok(z0)) → c24(RECIP(z0)) 333.60/104.18
SQR(mark(z0)) → c25(SQR(z0)) 333.60/104.18
SQR(ok(z0)) → c26(SQR(z0)) 333.60/104.18
S(mark(z0)) → c27(S(z0)) 333.60/104.18
S(ok(z0)) → c28(S(z0)) 333.60/104.18
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.60/104.18
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.60/104.18
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.60/104.18
DBL(mark(z0)) → c32(DBL(z0)) 333.60/104.18
DBL(ok(z0)) → c33(DBL(z0)) 333.60/104.18
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.60/104.18
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.60/104.18
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.60/104.18
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.60/104.18
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.60/104.18
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.60/104.18
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.60/104.18
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.60/104.18
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.60/104.18
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.60/104.18
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.60/104.18
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.60/104.18
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.60/104.18
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.60/104.18
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.60/104.18
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.60/104.18
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.60/104.18
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.60/104.18
ACTIVE(terms(z0)) → c1(S(z0)) 333.60/104.18
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.60/104.18
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.60/104.18
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.60/104.18
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 333.60/104.18
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.60/104.18
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.60/104.18
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.60/104.18
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.60/104.18
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.60/104.18
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.60/104.18
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.60/104.18
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.60/104.18
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.60/104.18
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.60/104.18
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.60/104.18
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.60/104.18
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.60/104.18
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.60/104.18
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.60/104.18
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.60/104.18
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.60/104.18
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.60/104.18
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 333.60/104.18
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.60/104.18
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.60/104.18
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.60/104.18
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.60/104.18
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.60/104.18
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.60/104.18
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)))) 333.60/104.18
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.60/104.18
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.60/104.18
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.60/104.18
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.60/104.18
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.60/104.18
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.60/104.18
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.60/104.18
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.60/104.18
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.60/104.18
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)) 333.60/104.18
ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 333.60/104.18
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 333.60/104.18
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.60/104.18
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.60/104.18
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.60/104.18
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.60/104.18
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.60/104.18
TERMS(mark(z0)) → c19(TERMS(z0)) 333.60/104.18
TERMS(ok(z0)) → c20(TERMS(z0)) 333.60/104.18
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.60/104.18
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.60/104.18
RECIP(mark(z0)) → c23(RECIP(z0)) 333.60/104.18
RECIP(ok(z0)) → c24(RECIP(z0)) 333.60/104.18
SQR(mark(z0)) → c25(SQR(z0)) 333.60/104.18
SQR(ok(z0)) → c26(SQR(z0)) 333.60/104.18
S(mark(z0)) → c27(S(z0)) 333.60/104.18
S(ok(z0)) → c28(S(z0)) 333.60/104.18
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.60/104.18
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.60/104.18
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.60/104.18
DBL(mark(z0)) → c32(DBL(z0)) 333.60/104.18
DBL(ok(z0)) → c33(DBL(z0)) 333.60/104.18
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.60/104.18
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.60/104.18
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.60/104.18
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.60/104.18
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.60/104.18
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.60/104.18
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.60/104.18
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.60/104.18
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.60/104.18
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.60/104.18
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.60/104.18
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.60/104.18
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.60/104.18
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.60/104.18
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.60/104.18
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.60/104.18
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.60/104.18
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.60/104.18
ACTIVE(terms(z0)) → c1(S(z0)) 333.60/104.18
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.60/104.18
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.60/104.18
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.60/104.18
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 333.60/104.18
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.60/104.18
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.60/104.18
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.60/104.18
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.60/104.18
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.60/104.18
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.60/104.18
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.60/104.18
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.60/104.18
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.60/104.18
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.60/104.18
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.60/104.18
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.60/104.18
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.60/104.18
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.60/104.18
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.60/104.18
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.60/104.18
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.60/104.18
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.60/104.18
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 333.60/104.18
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.60/104.18
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.60/104.18
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.60/104.18
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.60/104.18
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.60/104.18
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.60/104.18
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)))) 333.60/104.18
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.60/104.18
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.60/104.18
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.60/104.18
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.60/104.18
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.60/104.18
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.60/104.18
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.60/104.18
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.60/104.18
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.60/104.18
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, PROPER, 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, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10

333.60/104.18

(11) 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))) 333.99/104.21
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0)), ACTIVE(sqr(0))) 333.99/104.21
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.21
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.21
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.21
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.21
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.21
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.21
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.21
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.21
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.21
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.21
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.21
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.21
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.21
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.21
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.21
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.21
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

333.99/104.21

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 333.99/104.21
active(sqr(0)) → mark(0) 333.99/104.21
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 333.99/104.21
active(dbl(0)) → mark(0) 333.99/104.21
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 333.99/104.21
active(add(0, z0)) → mark(z0) 333.99/104.21
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 333.99/104.21
active(first(0, z0)) → mark(nil) 333.99/104.21
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 333.99/104.21
active(terms(z0)) → terms(active(z0)) 333.99/104.21
active(cons(z0, z1)) → cons(active(z0), z1) 333.99/104.21
active(recip(z0)) → recip(active(z0)) 333.99/104.21
active(sqr(z0)) → sqr(active(z0)) 333.99/104.21
active(s(z0)) → s(active(z0)) 333.99/104.21
active(add(z0, z1)) → add(active(z0), z1) 333.99/104.21
active(add(z0, z1)) → add(z0, active(z1)) 333.99/104.21
active(dbl(z0)) → dbl(active(z0)) 333.99/104.21
active(first(z0, z1)) → first(active(z0), z1) 333.99/104.21
active(first(z0, z1)) → first(z0, active(z1)) 333.99/104.21
terms(mark(z0)) → mark(terms(z0)) 333.99/104.21
terms(ok(z0)) → ok(terms(z0)) 333.99/104.21
cons(mark(z0), z1) → mark(cons(z0, z1)) 333.99/104.21
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 333.99/104.21
recip(mark(z0)) → mark(recip(z0)) 333.99/104.21
recip(ok(z0)) → ok(recip(z0)) 333.99/104.21
sqr(mark(z0)) → mark(sqr(z0)) 333.99/104.21
sqr(ok(z0)) → ok(sqr(z0)) 333.99/104.21
s(mark(z0)) → mark(s(z0)) 333.99/104.21
s(ok(z0)) → ok(s(z0)) 333.99/104.21
add(mark(z0), z1) → mark(add(z0, z1)) 333.99/104.21
add(z0, mark(z1)) → mark(add(z0, z1)) 333.99/104.21
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 333.99/104.21
dbl(mark(z0)) → mark(dbl(z0)) 333.99/104.21
dbl(ok(z0)) → ok(dbl(z0)) 333.99/104.21
first(mark(z0), z1) → mark(first(z0, z1)) 333.99/104.21
first(z0, mark(z1)) → mark(first(z0, z1)) 333.99/104.21
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 333.99/104.21
proper(terms(z0)) → terms(proper(z0)) 333.99/104.21
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 333.99/104.21
proper(recip(z0)) → recip(proper(z0)) 333.99/104.21
proper(sqr(z0)) → sqr(proper(z0)) 333.99/104.21
proper(s(z0)) → s(proper(z0)) 333.99/104.21
proper(0) → ok(0) 333.99/104.21
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 333.99/104.21
proper(dbl(z0)) → dbl(proper(z0)) 333.99/104.21
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 333.99/104.21
proper(nil) → ok(nil) 333.99/104.21
top(mark(z0)) → top(proper(z0)) 333.99/104.21
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sqr(z0)) → c12(SQR(active(z0)), ACTIVE(z0)) 333.99/104.21
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 333.99/104.21
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.21
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.21
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.99/104.21
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.21
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.21
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.21
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.21
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.21
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.21
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.21
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.21
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.21
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.21
S(mark(z0)) → c27(S(z0)) 333.99/104.21
S(ok(z0)) → c28(S(z0)) 333.99/104.21
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.21
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.21
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.21
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.21
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.21
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.21
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.21
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.21
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.21
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.21
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.21
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.21
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.21
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.21
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.21
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.21
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.21
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.21
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.21
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.21
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.21
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.21
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.21
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.21
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.21
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.21
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.21
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 333.99/104.21
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.21
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.21
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.21
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.21
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.21
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.21
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.21
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.21
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.21
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.21
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.21
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.21
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.21
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.21
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.21
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.21
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.21
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.21
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 333.99/104.21
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.21
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.21
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.21
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.21
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.21
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.21
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)))) 333.99/104.21
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.21
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.21
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.21
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.21
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.21
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.21
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.21
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.21
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.21
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.21
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.21
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0)), ACTIVE(sqr(0))) 333.99/104.21
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.21
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.21
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.21
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.21
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.21
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.21
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.21
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.21
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.21
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.21
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.21
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.21
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.21
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.21
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.21
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.21
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)) 333.99/104.21
ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 333.99/104.21
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.21
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.21
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.99/104.21
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.21
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.21
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.21
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.21
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.21
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.21
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.22
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.22
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.22
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.22
S(mark(z0)) → c27(S(z0)) 333.99/104.22
S(ok(z0)) → c28(S(z0)) 333.99/104.22
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.22
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.22
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.22
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.22
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.22
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.22
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.22
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.22
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.22
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.22
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.22
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.22
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.22
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)))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, PROPER, 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, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11

333.99/104.22

(13) 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))) 333.99/104.22
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))

333.99/104.22

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 333.99/104.22
active(sqr(0)) → mark(0) 333.99/104.22
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 333.99/104.22
active(dbl(0)) → mark(0) 333.99/104.22
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 333.99/104.22
active(add(0, z0)) → mark(z0) 333.99/104.22
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 333.99/104.22
active(first(0, z0)) → mark(nil) 333.99/104.22
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 333.99/104.22
active(terms(z0)) → terms(active(z0)) 333.99/104.22
active(cons(z0, z1)) → cons(active(z0), z1) 333.99/104.22
active(recip(z0)) → recip(active(z0)) 333.99/104.22
active(sqr(z0)) → sqr(active(z0)) 333.99/104.22
active(s(z0)) → s(active(z0)) 333.99/104.22
active(add(z0, z1)) → add(active(z0), z1) 333.99/104.22
active(add(z0, z1)) → add(z0, active(z1)) 333.99/104.22
active(dbl(z0)) → dbl(active(z0)) 333.99/104.22
active(first(z0, z1)) → first(active(z0), z1) 333.99/104.22
active(first(z0, z1)) → first(z0, active(z1)) 333.99/104.22
terms(mark(z0)) → mark(terms(z0)) 333.99/104.22
terms(ok(z0)) → ok(terms(z0)) 333.99/104.22
cons(mark(z0), z1) → mark(cons(z0, z1)) 333.99/104.22
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 333.99/104.22
recip(mark(z0)) → mark(recip(z0)) 333.99/104.22
recip(ok(z0)) → ok(recip(z0)) 333.99/104.22
sqr(mark(z0)) → mark(sqr(z0)) 333.99/104.22
sqr(ok(z0)) → ok(sqr(z0)) 333.99/104.22
s(mark(z0)) → mark(s(z0)) 333.99/104.22
s(ok(z0)) → ok(s(z0)) 333.99/104.22
add(mark(z0), z1) → mark(add(z0, z1)) 333.99/104.22
add(z0, mark(z1)) → mark(add(z0, z1)) 333.99/104.22
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 333.99/104.22
dbl(mark(z0)) → mark(dbl(z0)) 333.99/104.22
dbl(ok(z0)) → ok(dbl(z0)) 333.99/104.22
first(mark(z0), z1) → mark(first(z0, z1)) 333.99/104.22
first(z0, mark(z1)) → mark(first(z0, z1)) 333.99/104.22
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 333.99/104.22
proper(terms(z0)) → terms(proper(z0)) 333.99/104.22
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 333.99/104.22
proper(recip(z0)) → recip(proper(z0)) 333.99/104.22
proper(sqr(z0)) → sqr(proper(z0)) 333.99/104.22
proper(s(z0)) → s(proper(z0)) 333.99/104.22
proper(0) → ok(0) 333.99/104.22
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 333.99/104.22
proper(dbl(z0)) → dbl(proper(z0)) 333.99/104.22
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 333.99/104.22
proper(nil) → ok(nil) 333.99/104.22
top(mark(z0)) → top(proper(z0)) 333.99/104.22
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.22
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.22
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.22
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.22
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.22
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.22
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.22
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.22
S(mark(z0)) → c27(S(z0)) 333.99/104.22
S(ok(z0)) → c28(S(z0)) 333.99/104.22
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.22
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.22
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.22
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.22
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.22
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.22
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.22
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.22
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.22
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.22
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.22
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.22
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.22
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)))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))

S tuples:

ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.22
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.22
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.22
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.22
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.22
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.22
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.22
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.22
S(mark(z0)) → c27(S(z0)) 333.99/104.22
S(ok(z0)) → c28(S(z0)) 333.99/104.22
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.22
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.22
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.22
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.22
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.22
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.22
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.22
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.22
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.22
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.22
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.22
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.22
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.22
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)))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, PROPER, 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, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12

333.99/104.22

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

Removed 4 trailing tuple parts

333.99/104.22

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 333.99/104.22
active(sqr(0)) → mark(0) 333.99/104.22
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 333.99/104.22
active(dbl(0)) → mark(0) 333.99/104.22
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 333.99/104.22
active(add(0, z0)) → mark(z0) 333.99/104.22
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 333.99/104.22
active(first(0, z0)) → mark(nil) 333.99/104.22
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 333.99/104.22
active(terms(z0)) → terms(active(z0)) 333.99/104.22
active(cons(z0, z1)) → cons(active(z0), z1) 333.99/104.22
active(recip(z0)) → recip(active(z0)) 333.99/104.22
active(sqr(z0)) → sqr(active(z0)) 333.99/104.22
active(s(z0)) → s(active(z0)) 333.99/104.22
active(add(z0, z1)) → add(active(z0), z1) 333.99/104.22
active(add(z0, z1)) → add(z0, active(z1)) 333.99/104.22
active(dbl(z0)) → dbl(active(z0)) 333.99/104.22
active(first(z0, z1)) → first(active(z0), z1) 333.99/104.22
active(first(z0, z1)) → first(z0, active(z1)) 333.99/104.22
terms(mark(z0)) → mark(terms(z0)) 333.99/104.22
terms(ok(z0)) → ok(terms(z0)) 333.99/104.22
cons(mark(z0), z1) → mark(cons(z0, z1)) 333.99/104.22
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 333.99/104.22
recip(mark(z0)) → mark(recip(z0)) 333.99/104.22
recip(ok(z0)) → ok(recip(z0)) 333.99/104.22
sqr(mark(z0)) → mark(sqr(z0)) 333.99/104.22
sqr(ok(z0)) → ok(sqr(z0)) 333.99/104.22
s(mark(z0)) → mark(s(z0)) 333.99/104.22
s(ok(z0)) → ok(s(z0)) 333.99/104.22
add(mark(z0), z1) → mark(add(z0, z1)) 333.99/104.22
add(z0, mark(z1)) → mark(add(z0, z1)) 333.99/104.22
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 333.99/104.22
dbl(mark(z0)) → mark(dbl(z0)) 333.99/104.22
dbl(ok(z0)) → ok(dbl(z0)) 333.99/104.22
first(mark(z0), z1) → mark(first(z0, z1)) 333.99/104.22
first(z0, mark(z1)) → mark(first(z0, z1)) 333.99/104.22
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 333.99/104.22
proper(terms(z0)) → terms(proper(z0)) 333.99/104.22
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 333.99/104.22
proper(recip(z0)) → recip(proper(z0)) 333.99/104.22
proper(sqr(z0)) → sqr(proper(z0)) 333.99/104.22
proper(s(z0)) → s(proper(z0)) 333.99/104.22
proper(0) → ok(0) 333.99/104.22
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 333.99/104.22
proper(dbl(z0)) → dbl(proper(z0)) 333.99/104.22
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 333.99/104.22
proper(nil) → ok(nil) 333.99/104.22
top(mark(z0)) → top(proper(z0)) 333.99/104.22
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.22
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.22
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.22
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.22
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.22
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.22
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.22
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.22
S(mark(z0)) → c27(S(z0)) 333.99/104.22
S(ok(z0)) → c28(S(z0)) 333.99/104.22
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.22
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.22
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.22
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.22
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.22
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.22
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.22
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.22
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.22
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.22
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.22
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.22
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.22
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)))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.22
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.22
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.22
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0)))

S tuples:

ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.22
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.22
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.22
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.22
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.22
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.22
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.22
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.22
S(mark(z0)) → c27(S(z0)) 333.99/104.22
S(ok(z0)) → c28(S(z0)) 333.99/104.22
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.22
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.22
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.22
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.22
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.22
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.22
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.22
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.22
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.22
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.22
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.22
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.22
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.22
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)))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.22
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.22
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.22
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

ACTIVE, TERMS, CONS, RECIP, SQR, S, ADD, DBL, FIRST, PROPER, 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, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12

333.99/104.22

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

Use narrowing to replace ACTIVE(s(z0)) → c13(S(active(z0)), ACTIVE(z0)) by

ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(s(sqr(0))) → c13(S(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(s(dbl(0))) → c13(S(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))

333.99/104.22

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 333.99/104.22
active(sqr(0)) → mark(0) 333.99/104.22
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 333.99/104.22
active(dbl(0)) → mark(0) 333.99/104.22
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 333.99/104.22
active(add(0, z0)) → mark(z0) 333.99/104.22
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 333.99/104.22
active(first(0, z0)) → mark(nil) 333.99/104.22
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 333.99/104.22
active(terms(z0)) → terms(active(z0)) 333.99/104.22
active(cons(z0, z1)) → cons(active(z0), z1) 333.99/104.22
active(recip(z0)) → recip(active(z0)) 333.99/104.22
active(sqr(z0)) → sqr(active(z0)) 333.99/104.22
active(s(z0)) → s(active(z0)) 333.99/104.22
active(add(z0, z1)) → add(active(z0), z1) 333.99/104.22
active(add(z0, z1)) → add(z0, active(z1)) 333.99/104.22
active(dbl(z0)) → dbl(active(z0)) 333.99/104.22
active(first(z0, z1)) → first(active(z0), z1) 333.99/104.22
active(first(z0, z1)) → first(z0, active(z1)) 333.99/104.22
terms(mark(z0)) → mark(terms(z0)) 333.99/104.22
terms(ok(z0)) → ok(terms(z0)) 333.99/104.22
cons(mark(z0), z1) → mark(cons(z0, z1)) 333.99/104.22
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 333.99/104.22
recip(mark(z0)) → mark(recip(z0)) 333.99/104.22
recip(ok(z0)) → ok(recip(z0)) 333.99/104.22
sqr(mark(z0)) → mark(sqr(z0)) 333.99/104.22
sqr(ok(z0)) → ok(sqr(z0)) 333.99/104.22
s(mark(z0)) → mark(s(z0)) 333.99/104.22
s(ok(z0)) → ok(s(z0)) 333.99/104.22
add(mark(z0), z1) → mark(add(z0, z1)) 333.99/104.22
add(z0, mark(z1)) → mark(add(z0, z1)) 333.99/104.22
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 333.99/104.22
dbl(mark(z0)) → mark(dbl(z0)) 333.99/104.22
dbl(ok(z0)) → ok(dbl(z0)) 333.99/104.22
first(mark(z0), z1) → mark(first(z0, z1)) 333.99/104.22
first(z0, mark(z1)) → mark(first(z0, z1)) 333.99/104.22
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 333.99/104.22
proper(terms(z0)) → terms(proper(z0)) 333.99/104.22
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 333.99/104.22
proper(recip(z0)) → recip(proper(z0)) 333.99/104.22
proper(sqr(z0)) → sqr(proper(z0)) 333.99/104.22
proper(s(z0)) → s(proper(z0)) 333.99/104.22
proper(0) → ok(0) 333.99/104.22
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 333.99/104.22
proper(dbl(z0)) → dbl(proper(z0)) 333.99/104.22
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 333.99/104.22
proper(nil) → ok(nil) 333.99/104.22
top(mark(z0)) → top(proper(z0)) 333.99/104.22
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.22
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.22
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.22
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.22
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.22
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.22
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.22
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.22
S(mark(z0)) → c27(S(z0)) 333.99/104.22
S(ok(z0)) → c28(S(z0)) 333.99/104.22
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.22
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.22
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.22
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.22
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.22
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.22
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.22
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.22
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.22
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.22
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.22
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.22
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.22
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)))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.22
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.22
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.22
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.22
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(s(sqr(0))) → c13(S(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(s(dbl(0))) → c13(S(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.22
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.22
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.22
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.22
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.22
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.22
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.22
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.22
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.22
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.22
S(mark(z0)) → c27(S(z0)) 333.99/104.22
S(ok(z0)) → c28(S(z0)) 333.99/104.22
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.22
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.22
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.22
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.22
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.22
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.22
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.22
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.22
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.22
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.22
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.22
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.22
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.22
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.22
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.22
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.22
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.22
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.22
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)))) 333.99/104.22
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.22
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.22
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.22
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.22
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(s(sqr(0))) → c13(S(mark(0)), ACTIVE(sqr(0))) 333.99/104.22
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.22
ACTIVE(s(dbl(0))) → c13(S(mark(0)), ACTIVE(dbl(0))) 333.99/104.22
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.22
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.22
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.22
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.22
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.22
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.22
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.22
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.22
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.22
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.22
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.22
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.22
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.22
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13

333.99/104.23

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

Removed 1 trailing tuple parts

333.99/104.23

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 333.99/104.23
active(sqr(0)) → mark(0) 333.99/104.23
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 333.99/104.23
active(dbl(0)) → mark(0) 333.99/104.23
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 333.99/104.23
active(add(0, z0)) → mark(z0) 333.99/104.23
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 333.99/104.23
active(first(0, z0)) → mark(nil) 333.99/104.23
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 333.99/104.23
active(terms(z0)) → terms(active(z0)) 333.99/104.23
active(cons(z0, z1)) → cons(active(z0), z1) 333.99/104.23
active(recip(z0)) → recip(active(z0)) 333.99/104.23
active(sqr(z0)) → sqr(active(z0)) 333.99/104.23
active(s(z0)) → s(active(z0)) 333.99/104.23
active(add(z0, z1)) → add(active(z0), z1) 333.99/104.23
active(add(z0, z1)) → add(z0, active(z1)) 333.99/104.23
active(dbl(z0)) → dbl(active(z0)) 333.99/104.23
active(first(z0, z1)) → first(active(z0), z1) 333.99/104.23
active(first(z0, z1)) → first(z0, active(z1)) 333.99/104.23
terms(mark(z0)) → mark(terms(z0)) 333.99/104.23
terms(ok(z0)) → ok(terms(z0)) 333.99/104.23
cons(mark(z0), z1) → mark(cons(z0, z1)) 333.99/104.23
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 333.99/104.23
recip(mark(z0)) → mark(recip(z0)) 333.99/104.23
recip(ok(z0)) → ok(recip(z0)) 333.99/104.23
sqr(mark(z0)) → mark(sqr(z0)) 333.99/104.23
sqr(ok(z0)) → ok(sqr(z0)) 333.99/104.23
s(mark(z0)) → mark(s(z0)) 333.99/104.23
s(ok(z0)) → ok(s(z0)) 333.99/104.23
add(mark(z0), z1) → mark(add(z0, z1)) 333.99/104.23
add(z0, mark(z1)) → mark(add(z0, z1)) 333.99/104.23
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 333.99/104.23
dbl(mark(z0)) → mark(dbl(z0)) 333.99/104.23
dbl(ok(z0)) → ok(dbl(z0)) 333.99/104.23
first(mark(z0), z1) → mark(first(z0, z1)) 333.99/104.23
first(z0, mark(z1)) → mark(first(z0, z1)) 333.99/104.23
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 333.99/104.23
proper(terms(z0)) → terms(proper(z0)) 333.99/104.23
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 333.99/104.23
proper(recip(z0)) → recip(proper(z0)) 333.99/104.23
proper(sqr(z0)) → sqr(proper(z0)) 333.99/104.23
proper(s(z0)) → s(proper(z0)) 333.99/104.23
proper(0) → ok(0) 333.99/104.23
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 333.99/104.23
proper(dbl(z0)) → dbl(proper(z0)) 333.99/104.23
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 333.99/104.23
proper(nil) → ok(nil) 333.99/104.23
top(mark(z0)) → top(proper(z0)) 333.99/104.23
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.23
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.23
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.99/104.23
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.23
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.23
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.23
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.23
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.23
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.23
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.23
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.23
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.23
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.23
S(mark(z0)) → c27(S(z0)) 333.99/104.23
S(ok(z0)) → c28(S(z0)) 333.99/104.23
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.23
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.23
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.23
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.23
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.23
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.23
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.23
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.23
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.23
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.23
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.23
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.23
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.23
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.23
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.23
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.23
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.23
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.23
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.23
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.23
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.23
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.23
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.23
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.23
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.23
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.23
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.23
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.23
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.23
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.23
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.23
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.23
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.23
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.23
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.23
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.23
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.23
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.23
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.23
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.23
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.23
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.23
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.23
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.23
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.23
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.23
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.23
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.23
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.23
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.23
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.23
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)))) 333.99/104.23
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.23
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.23
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.23
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.23
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.23
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.23
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.23
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.23
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.23
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.23
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.23
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.23
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.23
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.23
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.23
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.23
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.23
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.23
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.23
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.23
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.23
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.23
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.23
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.23
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.23
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.23
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.23
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.23
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.23
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.23
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 333.99/104.23
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.23
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.23
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.23
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.23
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.23
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.23
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.23
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.23
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.23
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.23
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.23
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.23
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.23
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.23
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.23
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.23
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.23
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.23
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.23
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.23
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.23
ACTIVE(s(dbl(0))) → c13(S(mark(0)), ACTIVE(dbl(0))) 333.99/104.23
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.23
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.23
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.23
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.23
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.23
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.23
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.23
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.23
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.23
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.23
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.23
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.23
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.23
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.23
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.23
ACTIVE(s(sqr(0))) → c13(S(mark(0)))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.23
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.23
ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) 333.99/104.23
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.23
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.23
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.23
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.23
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.23
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.23
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.23
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.23
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.23
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.23
S(mark(z0)) → c27(S(z0)) 333.99/104.23
S(ok(z0)) → c28(S(z0)) 333.99/104.23
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.23
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.23
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.23
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.23
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.23
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.23
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.23
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.23
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.23
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.23
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.23
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.23
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.23
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.23
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.23
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.23
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.23
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.23
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.23
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.23
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.23
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.23
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.23
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.23
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.23
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.23
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.23
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.23
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.23
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.27
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)))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.27
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.27
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.27
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(s(dbl(0))) → c13(S(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(sqr(0))) → c13(S(mark(0)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13

333.99/104.27

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

Use narrowing to replace ACTIVE(dbl(z0)) → c16(DBL(active(z0)), ACTIVE(z0)) by

ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0)), ACTIVE(sqr(0))) 333.99/104.27
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))

333.99/104.27

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 333.99/104.27
active(sqr(0)) → mark(0) 333.99/104.27
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 333.99/104.27
active(dbl(0)) → mark(0) 333.99/104.27
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 333.99/104.27
active(add(0, z0)) → mark(z0) 333.99/104.27
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 333.99/104.27
active(first(0, z0)) → mark(nil) 333.99/104.27
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 333.99/104.27
active(terms(z0)) → terms(active(z0)) 333.99/104.27
active(cons(z0, z1)) → cons(active(z0), z1) 333.99/104.27
active(recip(z0)) → recip(active(z0)) 333.99/104.27
active(sqr(z0)) → sqr(active(z0)) 333.99/104.27
active(s(z0)) → s(active(z0)) 333.99/104.27
active(add(z0, z1)) → add(active(z0), z1) 333.99/104.27
active(add(z0, z1)) → add(z0, active(z1)) 333.99/104.27
active(dbl(z0)) → dbl(active(z0)) 333.99/104.27
active(first(z0, z1)) → first(active(z0), z1) 333.99/104.27
active(first(z0, z1)) → first(z0, active(z1)) 333.99/104.27
terms(mark(z0)) → mark(terms(z0)) 333.99/104.27
terms(ok(z0)) → ok(terms(z0)) 333.99/104.27
cons(mark(z0), z1) → mark(cons(z0, z1)) 333.99/104.27
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 333.99/104.27
recip(mark(z0)) → mark(recip(z0)) 333.99/104.27
recip(ok(z0)) → ok(recip(z0)) 333.99/104.27
sqr(mark(z0)) → mark(sqr(z0)) 333.99/104.27
sqr(ok(z0)) → ok(sqr(z0)) 333.99/104.27
s(mark(z0)) → mark(s(z0)) 333.99/104.27
s(ok(z0)) → ok(s(z0)) 333.99/104.27
add(mark(z0), z1) → mark(add(z0, z1)) 333.99/104.27
add(z0, mark(z1)) → mark(add(z0, z1)) 333.99/104.27
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 333.99/104.27
dbl(mark(z0)) → mark(dbl(z0)) 333.99/104.27
dbl(ok(z0)) → ok(dbl(z0)) 333.99/104.27
first(mark(z0), z1) → mark(first(z0, z1)) 333.99/104.27
first(z0, mark(z1)) → mark(first(z0, z1)) 333.99/104.27
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 333.99/104.27
proper(terms(z0)) → terms(proper(z0)) 333.99/104.27
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 333.99/104.27
proper(recip(z0)) → recip(proper(z0)) 333.99/104.27
proper(sqr(z0)) → sqr(proper(z0)) 333.99/104.27
proper(s(z0)) → s(proper(z0)) 333.99/104.27
proper(0) → ok(0) 333.99/104.27
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 333.99/104.27
proper(dbl(z0)) → dbl(proper(z0)) 333.99/104.27
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 333.99/104.27
proper(nil) → ok(nil) 333.99/104.27
top(mark(z0)) → top(proper(z0)) 333.99/104.27
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.27
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.27
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.27
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.27
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.27
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.27
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.27
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.27
S(mark(z0)) → c27(S(z0)) 333.99/104.27
S(ok(z0)) → c28(S(z0)) 333.99/104.27
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.27
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.27
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.27
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.27
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.27
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.27
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.27
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.27
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.27
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.27
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.27
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.27
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.27
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.27
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)))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.27
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.27
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.27
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(s(dbl(0))) → c13(S(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 333.99/104.27
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0)), ACTIVE(sqr(0))) 333.99/104.27
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.27
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.27
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.27
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.27
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.27
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.27
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.27
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.27
S(mark(z0)) → c27(S(z0)) 333.99/104.27
S(ok(z0)) → c28(S(z0)) 333.99/104.27
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.27
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.27
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.27
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.27
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.27
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.27
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.27
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.27
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.27
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.27
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.27
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.27
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.27
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.27
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)))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.27
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.27
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.27
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(s(dbl(0))) → c13(S(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 333.99/104.27
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0)), ACTIVE(sqr(0))) 333.99/104.27
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0)), ACTIVE(dbl(0))) 333.99/104.27
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16

333.99/104.27

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

Removed 7 trailing tuple parts

333.99/104.27

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 333.99/104.27
active(sqr(0)) → mark(0) 333.99/104.27
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 333.99/104.27
active(dbl(0)) → mark(0) 333.99/104.27
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 333.99/104.27
active(add(0, z0)) → mark(z0) 333.99/104.27
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 333.99/104.27
active(first(0, z0)) → mark(nil) 333.99/104.27
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 333.99/104.27
active(terms(z0)) → terms(active(z0)) 333.99/104.27
active(cons(z0, z1)) → cons(active(z0), z1) 333.99/104.27
active(recip(z0)) → recip(active(z0)) 333.99/104.27
active(sqr(z0)) → sqr(active(z0)) 333.99/104.27
active(s(z0)) → s(active(z0)) 333.99/104.27
active(add(z0, z1)) → add(active(z0), z1) 333.99/104.27
active(add(z0, z1)) → add(z0, active(z1)) 333.99/104.27
active(dbl(z0)) → dbl(active(z0)) 333.99/104.27
active(first(z0, z1)) → first(active(z0), z1) 333.99/104.27
active(first(z0, z1)) → first(z0, active(z1)) 333.99/104.27
terms(mark(z0)) → mark(terms(z0)) 333.99/104.27
terms(ok(z0)) → ok(terms(z0)) 333.99/104.27
cons(mark(z0), z1) → mark(cons(z0, z1)) 333.99/104.27
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 333.99/104.27
recip(mark(z0)) → mark(recip(z0)) 333.99/104.27
recip(ok(z0)) → ok(recip(z0)) 333.99/104.27
sqr(mark(z0)) → mark(sqr(z0)) 333.99/104.27
sqr(ok(z0)) → ok(sqr(z0)) 333.99/104.27
s(mark(z0)) → mark(s(z0)) 333.99/104.27
s(ok(z0)) → ok(s(z0)) 333.99/104.27
add(mark(z0), z1) → mark(add(z0, z1)) 333.99/104.27
add(z0, mark(z1)) → mark(add(z0, z1)) 333.99/104.27
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 333.99/104.27
dbl(mark(z0)) → mark(dbl(z0)) 333.99/104.27
dbl(ok(z0)) → ok(dbl(z0)) 333.99/104.27
first(mark(z0), z1) → mark(first(z0, z1)) 333.99/104.27
first(z0, mark(z1)) → mark(first(z0, z1)) 333.99/104.27
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 333.99/104.27
proper(terms(z0)) → terms(proper(z0)) 333.99/104.27
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 333.99/104.27
proper(recip(z0)) → recip(proper(z0)) 333.99/104.27
proper(sqr(z0)) → sqr(proper(z0)) 333.99/104.27
proper(s(z0)) → s(proper(z0)) 333.99/104.27
proper(0) → ok(0) 333.99/104.27
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 333.99/104.27
proper(dbl(z0)) → dbl(proper(z0)) 333.99/104.27
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 333.99/104.27
proper(nil) → ok(nil) 333.99/104.27
top(mark(z0)) → top(proper(z0)) 333.99/104.27
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.27
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.27
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.27
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.27
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.27
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.27
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.27
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.27
S(mark(z0)) → c27(S(z0)) 333.99/104.27
S(ok(z0)) → c28(S(z0)) 333.99/104.27
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.27
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.27
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.27
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.27
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.27
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.27
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.27
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.27
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.27
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.27
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.27
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.27
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.27
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.27
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)))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.27
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.27
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.27
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 333.99/104.27
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 333.99/104.27
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.27
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 333.99/104.27
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 333.99/104.27
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 333.99/104.27
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 333.99/104.27
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0)))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.27
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.27
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.27
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.27
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.27
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.27
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.27
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.27
S(mark(z0)) → c27(S(z0)) 333.99/104.27
S(ok(z0)) → c28(S(z0)) 333.99/104.27
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.27
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.27
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.27
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.27
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.27
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.27
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.27
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.27
PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.27
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.27
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.27
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.27
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.27
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.27
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)))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.27
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.27
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.27
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 333.99/104.27
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 333.99/104.27
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.27
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 333.99/104.27
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 333.99/104.27
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 333.99/104.27
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 333.99/104.27
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16

333.99/104.27

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

Use narrowing to replace PROPER(terms(z0)) → c37(TERMS(proper(z0)), PROPER(z0)) by

PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 333.99/104.27
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 333.99/104.27
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 333.99/104.27
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 333.99/104.27
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 333.99/104.27
PROPER(terms(0)) → c37(TERMS(ok(0)), PROPER(0)) 333.99/104.27
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 333.99/104.27
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 333.99/104.27
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 333.99/104.27
PROPER(terms(nil)) → c37(TERMS(ok(nil)), PROPER(nil))

333.99/104.27

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 333.99/104.27
active(sqr(0)) → mark(0) 333.99/104.27
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 333.99/104.27
active(dbl(0)) → mark(0) 333.99/104.27
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 333.99/104.27
active(add(0, z0)) → mark(z0) 333.99/104.27
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 333.99/104.27
active(first(0, z0)) → mark(nil) 333.99/104.27
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 333.99/104.27
active(terms(z0)) → terms(active(z0)) 333.99/104.27
active(cons(z0, z1)) → cons(active(z0), z1) 333.99/104.27
active(recip(z0)) → recip(active(z0)) 333.99/104.27
active(sqr(z0)) → sqr(active(z0)) 333.99/104.27
active(s(z0)) → s(active(z0)) 333.99/104.27
active(add(z0, z1)) → add(active(z0), z1) 333.99/104.27
active(add(z0, z1)) → add(z0, active(z1)) 333.99/104.27
active(dbl(z0)) → dbl(active(z0)) 333.99/104.27
active(first(z0, z1)) → first(active(z0), z1) 333.99/104.27
active(first(z0, z1)) → first(z0, active(z1)) 333.99/104.27
terms(mark(z0)) → mark(terms(z0)) 333.99/104.27
terms(ok(z0)) → ok(terms(z0)) 333.99/104.27
cons(mark(z0), z1) → mark(cons(z0, z1)) 333.99/104.27
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 333.99/104.27
recip(mark(z0)) → mark(recip(z0)) 333.99/104.27
recip(ok(z0)) → ok(recip(z0)) 333.99/104.27
sqr(mark(z0)) → mark(sqr(z0)) 333.99/104.27
sqr(ok(z0)) → ok(sqr(z0)) 333.99/104.27
s(mark(z0)) → mark(s(z0)) 333.99/104.27
s(ok(z0)) → ok(s(z0)) 333.99/104.27
add(mark(z0), z1) → mark(add(z0, z1)) 333.99/104.27
add(z0, mark(z1)) → mark(add(z0, z1)) 333.99/104.27
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 333.99/104.27
dbl(mark(z0)) → mark(dbl(z0)) 333.99/104.27
dbl(ok(z0)) → ok(dbl(z0)) 333.99/104.27
first(mark(z0), z1) → mark(first(z0, z1)) 333.99/104.27
first(z0, mark(z1)) → mark(first(z0, z1)) 333.99/104.27
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 333.99/104.27
proper(terms(z0)) → terms(proper(z0)) 333.99/104.27
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 333.99/104.27
proper(recip(z0)) → recip(proper(z0)) 333.99/104.27
proper(sqr(z0)) → sqr(proper(z0)) 333.99/104.27
proper(s(z0)) → s(proper(z0)) 333.99/104.27
proper(0) → ok(0) 333.99/104.27
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 333.99/104.27
proper(dbl(z0)) → dbl(proper(z0)) 333.99/104.27
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 333.99/104.27
proper(nil) → ok(nil) 333.99/104.27
top(mark(z0)) → top(proper(z0)) 333.99/104.27
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.27
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.27
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.27
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.27
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.27
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.27
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.27
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.27
S(mark(z0)) → c27(S(z0)) 333.99/104.27
S(ok(z0)) → c28(S(z0)) 333.99/104.27
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.27
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.27
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.27
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.27
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.27
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.27
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.27
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.27
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.27
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.27
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.27
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.27
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.27
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.27
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)))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.27
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.27
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.27
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 333.99/104.27
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 333.99/104.27
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.27
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 333.99/104.27
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 333.99/104.27
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 333.99/104.27
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 333.99/104.27
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 333.99/104.27
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 333.99/104.27
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 333.99/104.27
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 333.99/104.27
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 333.99/104.27
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 333.99/104.27
PROPER(terms(0)) → c37(TERMS(ok(0)), PROPER(0)) 333.99/104.27
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 333.99/104.27
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 333.99/104.27
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 333.99/104.27
PROPER(terms(nil)) → c37(TERMS(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.27
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.27
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.27
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.27
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.27
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.27
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.27
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.27
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.27
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.27
S(mark(z0)) → c27(S(z0)) 333.99/104.27
S(ok(z0)) → c28(S(z0)) 333.99/104.27
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.27
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.27
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.27
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.27
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.27
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.27
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.27
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.27
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.27
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.27
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.27
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.27
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.27
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.27
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.27
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.27
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.27
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.27
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)))) 333.99/104.27
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.27
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.27
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.27
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.27
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.27
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.27
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.27
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.27
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.27
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.27
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.27
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.28
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.28
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.28
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.28
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 333.99/104.28
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 333.99/104.28
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.28
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 333.99/104.28
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 333.99/104.28
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 333.99/104.28
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 333.99/104.28
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 333.99/104.28
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 333.99/104.28
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 333.99/104.28
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 333.99/104.28
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 333.99/104.28
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 333.99/104.28
PROPER(terms(0)) → c37(TERMS(ok(0)), PROPER(0)) 333.99/104.28
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 333.99/104.28
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 333.99/104.28
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 333.99/104.28
PROPER(terms(nil)) → c37(TERMS(ok(nil)), PROPER(nil))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37

333.99/104.28

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

Removed 2 trailing tuple parts

333.99/104.28

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 333.99/104.28
active(sqr(0)) → mark(0) 333.99/104.28
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 333.99/104.28
active(dbl(0)) → mark(0) 333.99/104.28
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 333.99/104.28
active(add(0, z0)) → mark(z0) 333.99/104.28
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 333.99/104.28
active(first(0, z0)) → mark(nil) 333.99/104.28
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 333.99/104.28
active(terms(z0)) → terms(active(z0)) 333.99/104.28
active(cons(z0, z1)) → cons(active(z0), z1) 333.99/104.28
active(recip(z0)) → recip(active(z0)) 333.99/104.28
active(sqr(z0)) → sqr(active(z0)) 333.99/104.28
active(s(z0)) → s(active(z0)) 333.99/104.28
active(add(z0, z1)) → add(active(z0), z1) 333.99/104.28
active(add(z0, z1)) → add(z0, active(z1)) 333.99/104.28
active(dbl(z0)) → dbl(active(z0)) 333.99/104.28
active(first(z0, z1)) → first(active(z0), z1) 333.99/104.28
active(first(z0, z1)) → first(z0, active(z1)) 333.99/104.28
terms(mark(z0)) → mark(terms(z0)) 333.99/104.28
terms(ok(z0)) → ok(terms(z0)) 333.99/104.28
cons(mark(z0), z1) → mark(cons(z0, z1)) 333.99/104.28
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 333.99/104.28
recip(mark(z0)) → mark(recip(z0)) 333.99/104.28
recip(ok(z0)) → ok(recip(z0)) 333.99/104.28
sqr(mark(z0)) → mark(sqr(z0)) 333.99/104.28
sqr(ok(z0)) → ok(sqr(z0)) 333.99/104.28
s(mark(z0)) → mark(s(z0)) 333.99/104.28
s(ok(z0)) → ok(s(z0)) 333.99/104.28
add(mark(z0), z1) → mark(add(z0, z1)) 333.99/104.28
add(z0, mark(z1)) → mark(add(z0, z1)) 333.99/104.28
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 333.99/104.28
dbl(mark(z0)) → mark(dbl(z0)) 333.99/104.28
dbl(ok(z0)) → ok(dbl(z0)) 333.99/104.28
first(mark(z0), z1) → mark(first(z0, z1)) 333.99/104.28
first(z0, mark(z1)) → mark(first(z0, z1)) 333.99/104.28
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 333.99/104.28
proper(terms(z0)) → terms(proper(z0)) 333.99/104.28
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 333.99/104.28
proper(recip(z0)) → recip(proper(z0)) 333.99/104.28
proper(sqr(z0)) → sqr(proper(z0)) 333.99/104.28
proper(s(z0)) → s(proper(z0)) 333.99/104.28
proper(0) → ok(0) 333.99/104.28
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 333.99/104.28
proper(dbl(z0)) → dbl(proper(z0)) 333.99/104.28
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 333.99/104.28
proper(nil) → ok(nil) 333.99/104.28
top(mark(z0)) → top(proper(z0)) 333.99/104.28
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.28
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.28
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.28
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.28
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.28
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.28
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.28
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.28
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.28
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.28
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.28
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.28
S(mark(z0)) → c27(S(z0)) 333.99/104.28
S(ok(z0)) → c28(S(z0)) 333.99/104.28
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.28
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.28
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.28
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.28
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.28
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.28
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.28
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.28
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.28
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.28
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.28
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.28
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.28
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.28
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.28
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.28
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.28
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.28
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.28
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.28
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.28
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.28
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)))) 333.99/104.28
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.28
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.28
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.28
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.28
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 333.99/104.28
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 333.99/104.28
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.28
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 333.99/104.28
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 333.99/104.28
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 333.99/104.28
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 333.99/104.28
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 333.99/104.28
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 333.99/104.28
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 333.99/104.28
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 333.99/104.28
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 333.99/104.28
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 333.99/104.28
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 333.99/104.28
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 333.99/104.28
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 333.99/104.28
PROPER(terms(0)) → c37(TERMS(ok(0))) 333.99/104.28
PROPER(terms(nil)) → c37(TERMS(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.28
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.28
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.28
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.28
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.28
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.28
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.28
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.28
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.28
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.28
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.28
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.28
S(mark(z0)) → c27(S(z0)) 333.99/104.28
S(ok(z0)) → c28(S(z0)) 333.99/104.28
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.28
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.28
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.28
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.28
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.28
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.28
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.28
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.28
PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.28
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.28
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.28
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.28
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.28
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.28
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.28
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.28
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.28
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.28
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.28
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.28
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.28
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.28
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)))) 333.99/104.28
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 333.99/104.28
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.28
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 333.99/104.28
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 333.99/104.28
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 333.99/104.28
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 333.99/104.28
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 333.99/104.28
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 333.99/104.28
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 333.99/104.28
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 333.99/104.28
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 333.99/104.28
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 333.99/104.28
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 333.99/104.28
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 333.99/104.28
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 333.99/104.28
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 333.99/104.28
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 333.99/104.28
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 333.99/104.28
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 333.99/104.28
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 333.99/104.28
PROPER(terms(0)) → c37(TERMS(ok(0))) 333.99/104.28
PROPER(terms(nil)) → c37(TERMS(ok(nil)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c38, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37

333.99/104.28

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

Use narrowing to replace PROPER(cons(z0, z1)) → c38(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 333.99/104.28
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 333.99/104.28
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 333.99/104.28
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 333.99/104.28
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 333.99/104.28
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 333.99/104.28
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 333.99/104.28
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 333.99/104.28
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 333.99/104.28
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 333.99/104.28
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 333.99/104.28
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 333.99/104.28
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 333.99/104.28
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 333.99/104.28
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 333.99/104.28
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 333.99/104.28
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 333.99/104.28
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 333.99/104.28
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 333.99/104.28
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

333.99/104.28

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 333.99/104.28
active(sqr(0)) → mark(0) 333.99/104.28
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 333.99/104.28
active(dbl(0)) → mark(0) 333.99/104.28
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 333.99/104.28
active(add(0, z0)) → mark(z0) 333.99/104.28
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 333.99/104.28
active(first(0, z0)) → mark(nil) 333.99/104.28
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 333.99/104.28
active(terms(z0)) → terms(active(z0)) 333.99/104.28
active(cons(z0, z1)) → cons(active(z0), z1) 333.99/104.28
active(recip(z0)) → recip(active(z0)) 333.99/104.28
active(sqr(z0)) → sqr(active(z0)) 333.99/104.28
active(s(z0)) → s(active(z0)) 333.99/104.28
active(add(z0, z1)) → add(active(z0), z1) 333.99/104.28
active(add(z0, z1)) → add(z0, active(z1)) 333.99/104.28
active(dbl(z0)) → dbl(active(z0)) 333.99/104.28
active(first(z0, z1)) → first(active(z0), z1) 333.99/104.28
active(first(z0, z1)) → first(z0, active(z1)) 333.99/104.28
terms(mark(z0)) → mark(terms(z0)) 333.99/104.28
terms(ok(z0)) → ok(terms(z0)) 333.99/104.28
cons(mark(z0), z1) → mark(cons(z0, z1)) 333.99/104.28
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 333.99/104.28
recip(mark(z0)) → mark(recip(z0)) 333.99/104.28
recip(ok(z0)) → ok(recip(z0)) 333.99/104.28
sqr(mark(z0)) → mark(sqr(z0)) 333.99/104.28
sqr(ok(z0)) → ok(sqr(z0)) 333.99/104.28
s(mark(z0)) → mark(s(z0)) 333.99/104.28
s(ok(z0)) → ok(s(z0)) 333.99/104.28
add(mark(z0), z1) → mark(add(z0, z1)) 333.99/104.28
add(z0, mark(z1)) → mark(add(z0, z1)) 333.99/104.28
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 333.99/104.28
dbl(mark(z0)) → mark(dbl(z0)) 333.99/104.28
dbl(ok(z0)) → ok(dbl(z0)) 333.99/104.28
first(mark(z0), z1) → mark(first(z0, z1)) 333.99/104.28
first(z0, mark(z1)) → mark(first(z0, z1)) 333.99/104.28
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 333.99/104.28
proper(terms(z0)) → terms(proper(z0)) 333.99/104.28
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 333.99/104.28
proper(recip(z0)) → recip(proper(z0)) 333.99/104.28
proper(sqr(z0)) → sqr(proper(z0)) 333.99/104.28
proper(s(z0)) → s(proper(z0)) 333.99/104.28
proper(0) → ok(0) 333.99/104.28
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 333.99/104.28
proper(dbl(z0)) → dbl(proper(z0)) 333.99/104.28
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 333.99/104.28
proper(nil) → ok(nil) 333.99/104.28
top(mark(z0)) → top(proper(z0)) 333.99/104.28
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 333.99/104.28
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 333.99/104.28
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 333.99/104.28
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 333.99/104.28
TERMS(mark(z0)) → c19(TERMS(z0)) 333.99/104.28
TERMS(ok(z0)) → c20(TERMS(z0)) 333.99/104.28
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 333.99/104.28
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 333.99/104.28
RECIP(mark(z0)) → c23(RECIP(z0)) 333.99/104.28
RECIP(ok(z0)) → c24(RECIP(z0)) 333.99/104.28
SQR(mark(z0)) → c25(SQR(z0)) 333.99/104.28
SQR(ok(z0)) → c26(SQR(z0)) 333.99/104.28
S(mark(z0)) → c27(S(z0)) 333.99/104.28
S(ok(z0)) → c28(S(z0)) 333.99/104.28
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 333.99/104.28
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 333.99/104.28
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 333.99/104.28
DBL(mark(z0)) → c32(DBL(z0)) 333.99/104.28
DBL(ok(z0)) → c33(DBL(z0)) 333.99/104.28
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 333.99/104.28
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 333.99/104.28
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 333.99/104.28
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.28
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 333.99/104.28
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 333.99/104.28
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 333.99/104.28
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 333.99/104.28
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 333.99/104.28
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 333.99/104.28
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 333.99/104.28
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 333.99/104.28
ACTIVE(terms(z0)) → c1(SQR(z0)) 333.99/104.28
ACTIVE(terms(z0)) → c1(S(z0)) 333.99/104.28
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 333.99/104.28
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 333.99/104.28
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 333.99/104.28
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 333.99/104.28
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 333.99/104.28
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 333.99/104.28
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 333.99/104.28
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 333.99/104.28
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 333.99/104.28
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 333.99/104.28
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 333.99/104.28
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 333.99/104.28
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 333.99/104.28
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 333.99/104.28
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 333.99/104.28
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 333.99/104.28
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 333.99/104.28
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)))) 333.99/104.28
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.30
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.30
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.30
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.30
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.30
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.30
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.30
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.30
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.30
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.30
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.30
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.30
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.30
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.30
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.30
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.30
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.30
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.30
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.30
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.30
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.30
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.30
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.30
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.30
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.30
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.30
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.30
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.30
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.30
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.30
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.30
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.30
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.30
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.30
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.30
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.30
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.30
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.30
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.30
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.30
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.30
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.30
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.30
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.30
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.30
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.30
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.30
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.30
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.30
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.30
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.30
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.30
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.30
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.30
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.30
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.30
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.30
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.30
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.30
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.30
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.30
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.30
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.30
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.30
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.30
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.30
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.30
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.30
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.30
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.30
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.30
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.30
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.30
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.30
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.30
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.30
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.34/104.30
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.30
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.30
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.30
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 334.34/104.30
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.30
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.30
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.30
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.30
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.30
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 334.34/104.30
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.30
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.30
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.30
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.30
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.30
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.30
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.30
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.30
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.30
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.30
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.30
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.30
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.30
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.30
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.30
S(mark(z0)) → c27(S(z0)) 334.34/104.30
S(ok(z0)) → c28(S(z0)) 334.34/104.30
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.30
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.30
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.30
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.30
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.30
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.30
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.30
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.30
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 334.34/104.30
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 334.34/104.30
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 334.34/104.30
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.30
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.30
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.30
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.30
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.30
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.30
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.30
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.30
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.30
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.30
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.30
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.30
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.30
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.30
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.30
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.30
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.30
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.30
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.30
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.30
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.30
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.30
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.30
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.30
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.30
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.30
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)))) 334.34/104.30
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.30
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.30
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.30
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.30
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.30
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.30
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.30
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.30
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.30
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.30
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.30
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.30
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.30
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.30
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.30
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.30
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.30
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.30
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.30
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.30
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.30
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.30
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.30
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.30
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.30
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.30
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.30
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.30
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.30
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.31
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.31
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.31
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.31
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.31
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.31
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.31
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.31
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.31
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.31
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.31
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.31
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.31
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.31
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.31
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.31
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.31
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.31
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.31
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.31
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.31
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.31
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.31
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.31
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.31
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.31
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.31
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.34/104.31
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.31
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.31
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.31
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 334.34/104.31
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.31
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 334.34/104.31
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.31
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.31
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38

334.34/104.31

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

Removed 4 trailing tuple parts

334.34/104.31

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.31
active(sqr(0)) → mark(0) 334.34/104.31
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.31
active(dbl(0)) → mark(0) 334.34/104.31
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.31
active(add(0, z0)) → mark(z0) 334.34/104.31
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.31
active(first(0, z0)) → mark(nil) 334.34/104.31
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.31
active(terms(z0)) → terms(active(z0)) 334.34/104.31
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.31
active(recip(z0)) → recip(active(z0)) 334.34/104.31
active(sqr(z0)) → sqr(active(z0)) 334.34/104.31
active(s(z0)) → s(active(z0)) 334.34/104.31
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.31
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.31
active(dbl(z0)) → dbl(active(z0)) 334.34/104.31
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.31
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.31
terms(mark(z0)) → mark(terms(z0)) 334.34/104.31
terms(ok(z0)) → ok(terms(z0)) 334.34/104.31
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.31
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.31
recip(mark(z0)) → mark(recip(z0)) 334.34/104.31
recip(ok(z0)) → ok(recip(z0)) 334.34/104.31
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.31
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.31
s(mark(z0)) → mark(s(z0)) 334.34/104.31
s(ok(z0)) → ok(s(z0)) 334.34/104.31
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.31
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.31
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.31
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.31
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.31
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.31
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.31
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.31
proper(terms(z0)) → terms(proper(z0)) 334.34/104.31
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.31
proper(recip(z0)) → recip(proper(z0)) 334.34/104.31
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.31
proper(s(z0)) → s(proper(z0)) 334.34/104.31
proper(0) → ok(0) 334.34/104.31
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.31
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.31
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.31
proper(nil) → ok(nil) 334.34/104.31
top(mark(z0)) → top(proper(z0)) 334.34/104.31
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.31
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.31
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.31
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.31
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.31
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.31
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.31
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.31
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.31
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.31
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.31
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.31
S(mark(z0)) → c27(S(z0)) 334.34/104.31
S(ok(z0)) → c28(S(z0)) 334.34/104.31
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.31
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.31
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.31
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.31
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.31
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.31
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.31
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.31
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 334.34/104.31
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 334.34/104.31
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 334.34/104.31
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.31
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.31
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.31
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.31
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.31
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.31
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.31
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.31
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.31
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.31
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.31
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.31
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)))) 334.34/104.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.31
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.31
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.31
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.31
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.31
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.31
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.31
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.31
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.31
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.31
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.31
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.31
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.31
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.31
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.31
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.31
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.31
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.31
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.31
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.31
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.31
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.31
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.31
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.31
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.31
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.31
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.31
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.31
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.31
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.31
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.31
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.31
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.31
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.31
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.31
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.31
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.31
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.31
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.31
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.31
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.31
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.31
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.31
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.31
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.31
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.31
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.31
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.31
S(mark(z0)) → c27(S(z0)) 334.34/104.31
S(ok(z0)) → c28(S(z0)) 334.34/104.31
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.31
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.31
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.31
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.31
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.31
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.31
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.31
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.31
PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) 334.34/104.31
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 334.34/104.31
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 334.34/104.31
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.31
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.31
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.31
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.31
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.31
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.31
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.31
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.31
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.31
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.31
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.31
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.31
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)))) 334.34/104.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.31
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.31
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.31
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.31
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.31
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.31
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.31
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.31
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.31
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.31
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.31
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.31
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.31
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.31
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.31
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.31
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.31
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.31
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.31
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.31
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.31
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.31
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.31
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.31
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.31
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.31
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.31
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.31
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.31
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.31
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.31
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.31
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.31
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.31
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.31
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.31
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.31
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c39, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38

334.34/104.31

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

Use narrowing to replace PROPER(recip(z0)) → c39(RECIP(proper(z0)), PROPER(z0)) by

PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.31
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.31
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.31
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.31
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.31
PROPER(recip(0)) → c39(RECIP(ok(0)), PROPER(0)) 334.34/104.31
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.31
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.31
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.31
PROPER(recip(nil)) → c39(RECIP(ok(nil)), PROPER(nil))

334.34/104.31

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.31
active(sqr(0)) → mark(0) 334.34/104.31
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.31
active(dbl(0)) → mark(0) 334.34/104.31
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.31
active(add(0, z0)) → mark(z0) 334.34/104.31
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.31
active(first(0, z0)) → mark(nil) 334.34/104.31
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.31
active(terms(z0)) → terms(active(z0)) 334.34/104.31
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.31
active(recip(z0)) → recip(active(z0)) 334.34/104.31
active(sqr(z0)) → sqr(active(z0)) 334.34/104.31
active(s(z0)) → s(active(z0)) 334.34/104.31
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.31
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.31
active(dbl(z0)) → dbl(active(z0)) 334.34/104.31
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.31
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.31
terms(mark(z0)) → mark(terms(z0)) 334.34/104.31
terms(ok(z0)) → ok(terms(z0)) 334.34/104.31
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.31
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.31
recip(mark(z0)) → mark(recip(z0)) 334.34/104.31
recip(ok(z0)) → ok(recip(z0)) 334.34/104.31
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.31
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.31
s(mark(z0)) → mark(s(z0)) 334.34/104.31
s(ok(z0)) → ok(s(z0)) 334.34/104.31
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.31
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.31
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.31
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.31
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.31
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.31
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.31
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.31
proper(terms(z0)) → terms(proper(z0)) 334.34/104.31
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.31
proper(recip(z0)) → recip(proper(z0)) 334.34/104.31
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.31
proper(s(z0)) → s(proper(z0)) 334.34/104.31
proper(0) → ok(0) 334.34/104.31
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.31
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.31
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.31
proper(nil) → ok(nil) 334.34/104.31
top(mark(z0)) → top(proper(z0)) 334.34/104.31
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.31
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.31
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.31
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.31
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.31
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.31
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.31
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.31
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.31
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.31
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.31
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.31
S(mark(z0)) → c27(S(z0)) 334.34/104.31
S(ok(z0)) → c28(S(z0)) 334.34/104.31
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.31
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.31
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.31
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.31
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.31
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.31
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.31
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.31
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 334.34/104.31
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 334.34/104.31
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.31
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.31
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.31
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.31
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.31
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.31
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.31
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.31
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.31
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.31
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.31
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.31
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.31
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)))) 334.34/104.31
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.31
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.31
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.31
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.31
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.31
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.31
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.31
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.31
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.31
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.31
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.31
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.31
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.33
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.33
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.33
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.33
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.33
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.33
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.33
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.33
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.33
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.33
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.33
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.33
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.33
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.33
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.33
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.33
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.33
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.33
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.33
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.33
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.33
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.33
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.33
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.33
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.33
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.33
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.33
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.33
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.33
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.33
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.33
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.33
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.33
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.33
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.33
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.33
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.33
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.33
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.33
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.33
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.33
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.33
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.33
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.33
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.33
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.33
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.33
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.33
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.33
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.33
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.33
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.33
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.33
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.33
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.33
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.33
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.33
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.33
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.33
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.33
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.33
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.33
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.33
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.33
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.33
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.33
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.33
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.33
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.33
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.33
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.33
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.33
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.33
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.33
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.33
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.33
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.33
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.33
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.33
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.33
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.33
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.33
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.33
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.33
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.33
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.33
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.33
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.33
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.33
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.33
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.33
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.33
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.33
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.33
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.33
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.33
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.33
PROPER(recip(0)) → c39(RECIP(ok(0)), PROPER(0)) 334.34/104.33
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.33
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.33
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.33
PROPER(recip(nil)) → c39(RECIP(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.33
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.33
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.33
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.33
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.33
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.33
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.33
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.33
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.33
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.33
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.33
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.33
S(mark(z0)) → c27(S(z0)) 334.34/104.33
S(ok(z0)) → c28(S(z0)) 334.34/104.33
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.33
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.33
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.33
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.33
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.33
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.33
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.33
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.33
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 334.34/104.33
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 334.34/104.33
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.33
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.33
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.33
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.33
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.33
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.33
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.33
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.33
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.33
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.33
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.33
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.33
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.33
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.33
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.33
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.33
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.33
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.33
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.33
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.33
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.33
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.34
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)))) 334.34/104.34
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.34
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.34
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.34
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.34
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.34
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.34
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.34
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.34
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.34
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.34
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.34
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.34
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.34
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.34
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.34
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.34
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.34
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.34
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.34
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.34
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.34
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.34
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.34
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.34
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.34
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.34
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.34
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.34
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.34
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.34
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.34
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.34
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.34
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.34
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.34
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.34
PROPER(recip(0)) → c39(RECIP(ok(0)), PROPER(0)) 334.34/104.34
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.34
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.34
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.34
PROPER(recip(nil)) → c39(RECIP(ok(nil)), PROPER(nil))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39

334.34/104.34

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

Removed 2 trailing tuple parts

334.34/104.34

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.34
active(sqr(0)) → mark(0) 334.34/104.34
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.34
active(dbl(0)) → mark(0) 334.34/104.34
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.34
active(add(0, z0)) → mark(z0) 334.34/104.34
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.34
active(first(0, z0)) → mark(nil) 334.34/104.34
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.34
active(terms(z0)) → terms(active(z0)) 334.34/104.34
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.34
active(recip(z0)) → recip(active(z0)) 334.34/104.34
active(sqr(z0)) → sqr(active(z0)) 334.34/104.34
active(s(z0)) → s(active(z0)) 334.34/104.34
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.34
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.34
active(dbl(z0)) → dbl(active(z0)) 334.34/104.34
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.34
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.34
terms(mark(z0)) → mark(terms(z0)) 334.34/104.34
terms(ok(z0)) → ok(terms(z0)) 334.34/104.34
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.34
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.34
recip(mark(z0)) → mark(recip(z0)) 334.34/104.34
recip(ok(z0)) → ok(recip(z0)) 334.34/104.34
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.34
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.34
s(mark(z0)) → mark(s(z0)) 334.34/104.34
s(ok(z0)) → ok(s(z0)) 334.34/104.34
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.34
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.34
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.34
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.34
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.34
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.34
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.34
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.34
proper(terms(z0)) → terms(proper(z0)) 334.34/104.34
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.34
proper(recip(z0)) → recip(proper(z0)) 334.34/104.34
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.34
proper(s(z0)) → s(proper(z0)) 334.34/104.34
proper(0) → ok(0) 334.34/104.34
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.34
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.34
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.34
proper(nil) → ok(nil) 334.34/104.34
top(mark(z0)) → top(proper(z0)) 334.34/104.34
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.34
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.34
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.34
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.34
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.34
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.34
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.34
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.34
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.34
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.34
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.34
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.34
S(mark(z0)) → c27(S(z0)) 334.34/104.34
S(ok(z0)) → c28(S(z0)) 334.34/104.34
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.34
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.34
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.34
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.34
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.34
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.34
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.34
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.34
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 334.34/104.34
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 334.34/104.34
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.34
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.34
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.34
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.34
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.34
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.34
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.34
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.34
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.34
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.34
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.34
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.34
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)))) 334.34/104.34
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.34
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.34
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.34
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.34
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.34
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.34
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.34
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.34
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.34
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.34
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.34
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.34
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.34
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.34
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.34
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.34
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.34
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.34
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.34
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.34
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.34
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.34
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.34
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.34
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.34
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.34
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.34
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.34
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.34
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.34
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.34
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.34
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.34
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.34
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.34
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.34
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.34
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.34
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.34
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.34
PROPER(recip(nil)) → c39(RECIP(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.34
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.34
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.34
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.34
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.34
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.34
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.34
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.34
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.34
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.34
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.34
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.34
S(mark(z0)) → c27(S(z0)) 334.34/104.34
S(ok(z0)) → c28(S(z0)) 334.34/104.34
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.34
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.34
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.34
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.34
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.34
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.34
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.34
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.34
PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) 334.34/104.34
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 334.34/104.34
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.34
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.34
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.34
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.34
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.34
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.34
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.34
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.34
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.34
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.34
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.34
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.34
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)))) 334.34/104.34
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.34
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.34
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.34
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.34
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.34
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.34
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.34
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.34
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.34
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.34
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.34
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.34
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.34
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.34
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.34
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.34
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.34
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.34
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.34
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.34
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.34
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.34
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.34
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.34
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.34
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.34
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.34
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.34
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.34
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.34
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.34
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.34
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.34
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.34
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.34
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.34
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.34
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.34
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.34
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.34
PROPER(recip(nil)) → c39(RECIP(ok(nil)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c40, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39

334.34/104.34

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

Use narrowing to replace PROPER(sqr(z0)) → c40(SQR(proper(z0)), PROPER(z0)) by

PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.34
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.34
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.34
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.34
PROPER(sqr(0)) → c40(SQR(ok(0)), PROPER(0)) 334.34/104.34
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.34
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.34
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.34
PROPER(sqr(nil)) → c40(SQR(ok(nil)), PROPER(nil))

334.34/104.34

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.34
active(sqr(0)) → mark(0) 334.34/104.34
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.34
active(dbl(0)) → mark(0) 334.34/104.34
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.34
active(add(0, z0)) → mark(z0) 334.34/104.34
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.34
active(first(0, z0)) → mark(nil) 334.34/104.34
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.34
active(terms(z0)) → terms(active(z0)) 334.34/104.34
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.34
active(recip(z0)) → recip(active(z0)) 334.34/104.34
active(sqr(z0)) → sqr(active(z0)) 334.34/104.34
active(s(z0)) → s(active(z0)) 334.34/104.34
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.34
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.34
active(dbl(z0)) → dbl(active(z0)) 334.34/104.34
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.34
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.34
terms(mark(z0)) → mark(terms(z0)) 334.34/104.34
terms(ok(z0)) → ok(terms(z0)) 334.34/104.34
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.34
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.34
recip(mark(z0)) → mark(recip(z0)) 334.34/104.34
recip(ok(z0)) → ok(recip(z0)) 334.34/104.34
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.34
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.34
s(mark(z0)) → mark(s(z0)) 334.34/104.34
s(ok(z0)) → ok(s(z0)) 334.34/104.34
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.34
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.34
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.34
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.34
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.34
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.34
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.34
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.34
proper(terms(z0)) → terms(proper(z0)) 334.34/104.34
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.34
proper(recip(z0)) → recip(proper(z0)) 334.34/104.34
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.34
proper(s(z0)) → s(proper(z0)) 334.34/104.34
proper(0) → ok(0) 334.34/104.34
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.34
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.34
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.34
proper(nil) → ok(nil) 334.34/104.34
top(mark(z0)) → top(proper(z0)) 334.34/104.34
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.34
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.34
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.34
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.34
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.34
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.34
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.34
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.34
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.34
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.34
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.34
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.34
S(mark(z0)) → c27(S(z0)) 334.34/104.34
S(ok(z0)) → c28(S(z0)) 334.34/104.34
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.34
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.34
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.34
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.34
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.34
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.34
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.34
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.34
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 334.34/104.34
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.34
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.34
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.34
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.34
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.34
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.34
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.34
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.34
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.34
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.34
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.34
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.34
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)))) 334.34/104.34
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.34
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.34
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.34
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.34
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.34
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.34
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.34
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.34
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.34
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.34
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.34
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.34
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.34
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.34
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.34
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.34
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.34
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.34
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.34
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.34
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.34
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.34
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.34
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.34
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.34
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.34
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.34
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.34
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.34
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.34
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.34
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.34
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.34
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.34
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.34
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.34
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.34
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.34
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.34
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.34
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.34
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.34
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.34
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.34
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.34
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.34
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.34
PROPER(sqr(0)) → c40(SQR(ok(0)), PROPER(0)) 334.34/104.34
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.34
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.34
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.34
PROPER(sqr(nil)) → c40(SQR(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.34
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.34
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.34
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.34
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.34
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.34
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.34
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.34
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.34
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.34
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.34
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.34
S(mark(z0)) → c27(S(z0)) 334.34/104.34
S(ok(z0)) → c28(S(z0)) 334.34/104.34
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.34
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.34
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.34
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.34
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.34
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.34
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.34
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.34
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 334.34/104.34
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.34
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.34
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.34
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.34
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.34
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.34
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.34
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.34
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.34
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.34
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.34
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.34
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.34
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)))) 334.34/104.34
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.34
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.34
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.34
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.34
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.34
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.34
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.34
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.34
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.34
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.34
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.34
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.34
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.34
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.34
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.34
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.34
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.34
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.34
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.34
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.34
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.34
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.34
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.34
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.34
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.34
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.34
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.34
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.34
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.34
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.34
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.34
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.34
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.34
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.34
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.34
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.34
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.34
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.34
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.34
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.34
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.35
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.35
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.35
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.35
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.35
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.35
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.35
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(sqr(0)) → c40(SQR(ok(0)), PROPER(0)) 334.34/104.35
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(sqr(nil)) → c40(SQR(ok(nil)), PROPER(nil))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40

334.34/104.35

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

Removed 2 trailing tuple parts

334.34/104.35

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.35
active(sqr(0)) → mark(0) 334.34/104.35
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.35
active(dbl(0)) → mark(0) 334.34/104.35
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.35
active(add(0, z0)) → mark(z0) 334.34/104.35
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.35
active(first(0, z0)) → mark(nil) 334.34/104.35
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.35
active(terms(z0)) → terms(active(z0)) 334.34/104.35
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.35
active(recip(z0)) → recip(active(z0)) 334.34/104.35
active(sqr(z0)) → sqr(active(z0)) 334.34/104.35
active(s(z0)) → s(active(z0)) 334.34/104.35
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.35
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.35
active(dbl(z0)) → dbl(active(z0)) 334.34/104.35
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.35
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.35
terms(mark(z0)) → mark(terms(z0)) 334.34/104.35
terms(ok(z0)) → ok(terms(z0)) 334.34/104.35
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.35
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.35
recip(mark(z0)) → mark(recip(z0)) 334.34/104.35
recip(ok(z0)) → ok(recip(z0)) 334.34/104.35
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.35
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.35
s(mark(z0)) → mark(s(z0)) 334.34/104.35
s(ok(z0)) → ok(s(z0)) 334.34/104.35
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.35
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.35
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.35
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.35
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.35
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.35
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.35
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.35
proper(terms(z0)) → terms(proper(z0)) 334.34/104.35
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.35
proper(recip(z0)) → recip(proper(z0)) 334.34/104.35
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.35
proper(s(z0)) → s(proper(z0)) 334.34/104.35
proper(0) → ok(0) 334.34/104.35
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.35
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.35
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.35
proper(nil) → ok(nil) 334.34/104.35
top(mark(z0)) → top(proper(z0)) 334.34/104.35
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.35
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.35
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.35
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.35
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.35
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.35
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.35
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.35
S(mark(z0)) → c27(S(z0)) 334.34/104.35
S(ok(z0)) → c28(S(z0)) 334.34/104.35
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.35
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.35
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.35
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.35
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.35
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.35
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.35
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.35
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 334.34/104.35
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.35
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.35
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.35
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.35
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.35
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.35
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.35
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)))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.35
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.35
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.35
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.35
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.35
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.35
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.35
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.35
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.35
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.35
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.35
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.35
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.35
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.35
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.35
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.35
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.35
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.35
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.35
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.35
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.35
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.35
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.35
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.35
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.35
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.35
PROPER(sqr(nil)) → c40(SQR(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.35
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.35
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.35
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.35
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.35
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.35
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.35
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.35
S(mark(z0)) → c27(S(z0)) 334.34/104.35
S(ok(z0)) → c28(S(z0)) 334.34/104.35
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.35
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.35
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.35
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.35
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.35
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.35
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.35
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.35
PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) 334.34/104.35
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.35
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.35
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.35
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.35
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.35
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.35
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.35
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)))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.35
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.35
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.35
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.35
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.35
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.35
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.35
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.35
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.35
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.35
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.35
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.35
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.35
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.35
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.35
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.35
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.35
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.35
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.35
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.35
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.35
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.35
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.35
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.35
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.35
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.35
PROPER(sqr(nil)) → c40(SQR(ok(nil)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c41, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40

334.34/104.35

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

Use narrowing to replace PROPER(s(z0)) → c41(S(proper(z0)), PROPER(z0)) by

PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(s(0)) → c41(S(ok(0)), PROPER(0)) 334.34/104.35
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(s(nil)) → c41(S(ok(nil)), PROPER(nil))

334.34/104.35

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.35
active(sqr(0)) → mark(0) 334.34/104.35
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.35
active(dbl(0)) → mark(0) 334.34/104.35
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.35
active(add(0, z0)) → mark(z0) 334.34/104.35
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.35
active(first(0, z0)) → mark(nil) 334.34/104.35
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.35
active(terms(z0)) → terms(active(z0)) 334.34/104.35
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.35
active(recip(z0)) → recip(active(z0)) 334.34/104.35
active(sqr(z0)) → sqr(active(z0)) 334.34/104.35
active(s(z0)) → s(active(z0)) 334.34/104.35
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.35
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.35
active(dbl(z0)) → dbl(active(z0)) 334.34/104.35
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.35
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.35
terms(mark(z0)) → mark(terms(z0)) 334.34/104.35
terms(ok(z0)) → ok(terms(z0)) 334.34/104.35
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.35
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.35
recip(mark(z0)) → mark(recip(z0)) 334.34/104.35
recip(ok(z0)) → ok(recip(z0)) 334.34/104.35
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.35
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.35
s(mark(z0)) → mark(s(z0)) 334.34/104.35
s(ok(z0)) → ok(s(z0)) 334.34/104.35
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.35
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.35
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.35
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.35
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.35
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.35
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.35
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.35
proper(terms(z0)) → terms(proper(z0)) 334.34/104.35
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.35
proper(recip(z0)) → recip(proper(z0)) 334.34/104.35
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.35
proper(s(z0)) → s(proper(z0)) 334.34/104.35
proper(0) → ok(0) 334.34/104.35
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.35
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.35
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.35
proper(nil) → ok(nil) 334.34/104.35
top(mark(z0)) → top(proper(z0)) 334.34/104.35
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.35
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.35
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.35
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.35
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.35
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.35
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.35
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.35
S(mark(z0)) → c27(S(z0)) 334.34/104.35
S(ok(z0)) → c28(S(z0)) 334.34/104.35
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.35
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.35
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.35
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.35
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.35
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.35
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.35
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.35
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.35
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.35
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.35
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.35
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.35
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.35
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.35
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)))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.35
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.35
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.35
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.35
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.35
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.35
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.35
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.35
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.35
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.35
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.35
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.35
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.35
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.35
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.35
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.35
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.35
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.35
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.35
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.35
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.35
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.35
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.35
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.35
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.35
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.35
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.35
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(s(0)) → c41(S(ok(0)), PROPER(0)) 334.34/104.35
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(s(nil)) → c41(S(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.35
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.35
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.35
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.35
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.35
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.35
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.35
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.35
S(mark(z0)) → c27(S(z0)) 334.34/104.35
S(ok(z0)) → c28(S(z0)) 334.34/104.35
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.35
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.35
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.35
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.35
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.35
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.35
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.35
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.35
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.35
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.35
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.35
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.35
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.35
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.35
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.35
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)))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.35
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.35
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.35
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.35
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.35
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.35
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.35
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.35
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.35
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.35
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.35
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.35
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.35
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.35
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.35
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.35
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.35
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.35
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.35
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.35
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.35
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.35
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.35
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.35
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.35
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.35
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.35
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(s(0)) → c41(S(ok(0)), PROPER(0)) 334.34/104.35
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(s(nil)) → c41(S(ok(nil)), PROPER(nil))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40, c41

334.34/104.35

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

Removed 2 trailing tuple parts

334.34/104.35

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.35
active(sqr(0)) → mark(0) 334.34/104.35
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.35
active(dbl(0)) → mark(0) 334.34/104.35
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.35
active(add(0, z0)) → mark(z0) 334.34/104.35
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.35
active(first(0, z0)) → mark(nil) 334.34/104.35
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.35
active(terms(z0)) → terms(active(z0)) 334.34/104.35
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.35
active(recip(z0)) → recip(active(z0)) 334.34/104.35
active(sqr(z0)) → sqr(active(z0)) 334.34/104.35
active(s(z0)) → s(active(z0)) 334.34/104.35
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.35
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.35
active(dbl(z0)) → dbl(active(z0)) 334.34/104.35
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.35
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.35
terms(mark(z0)) → mark(terms(z0)) 334.34/104.35
terms(ok(z0)) → ok(terms(z0)) 334.34/104.35
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.35
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.35
recip(mark(z0)) → mark(recip(z0)) 334.34/104.35
recip(ok(z0)) → ok(recip(z0)) 334.34/104.35
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.35
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.35
s(mark(z0)) → mark(s(z0)) 334.34/104.35
s(ok(z0)) → ok(s(z0)) 334.34/104.35
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.35
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.35
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.35
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.35
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.35
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.35
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.35
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.35
proper(terms(z0)) → terms(proper(z0)) 334.34/104.35
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.35
proper(recip(z0)) → recip(proper(z0)) 334.34/104.35
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.35
proper(s(z0)) → s(proper(z0)) 334.34/104.35
proper(0) → ok(0) 334.34/104.35
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.35
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.35
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.35
proper(nil) → ok(nil) 334.34/104.35
top(mark(z0)) → top(proper(z0)) 334.34/104.35
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.35
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.35
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.35
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.35
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.35
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.35
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.35
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.35
S(mark(z0)) → c27(S(z0)) 334.34/104.35
S(ok(z0)) → c28(S(z0)) 334.34/104.35
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.35
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.35
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.35
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.35
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.35
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.35
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.35
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.35
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.35
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.35
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.35
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.35
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.35
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.35
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.35
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)))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.35
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.35
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.35
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.35
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.35
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.35
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.35
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.35
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.35
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.35
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.35
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.35
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.35
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.35
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.35
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.35
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.35
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.35
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.35
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.35
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.35
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.35
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.35
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.35
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.35
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.35
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.35
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.35
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.35
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.35
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.35
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.35
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.35
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.35
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.35
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.35
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.35
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.35
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.35
PROPER(s(nil)) → c41(S(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.35
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.35
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.35
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.35
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.35
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.35
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.35
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.35
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.35
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.35
S(mark(z0)) → c27(S(z0)) 334.34/104.35
S(ok(z0)) → c28(S(z0)) 334.34/104.35
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.35
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.35
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.35
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.35
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.35
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.35
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.35
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.35
PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.35
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.35
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.35
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.35
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.35
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.35
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.35
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.35
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.35
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.35
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.35
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.35
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.35
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.35
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.35
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.35
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)))) 334.34/104.35
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.35
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.35
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.35
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.35
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.35
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.36
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.36
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.36
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.36
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.36
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.36
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.36
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.36
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.36
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.36
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.36
PROPER(s(nil)) → c41(S(ok(nil)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c43, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40, c41, c41

334.34/104.36

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

Use narrowing to replace PROPER(add(z0, z1)) → c43(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.34/104.36
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 334.34/104.36
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 334.34/104.36
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

334.34/104.36

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.36
active(sqr(0)) → mark(0) 334.34/104.36
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.36
active(dbl(0)) → mark(0) 334.34/104.36
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.36
active(add(0, z0)) → mark(z0) 334.34/104.36
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.36
active(first(0, z0)) → mark(nil) 334.34/104.36
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.36
active(terms(z0)) → terms(active(z0)) 334.34/104.36
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.36
active(recip(z0)) → recip(active(z0)) 334.34/104.36
active(sqr(z0)) → sqr(active(z0)) 334.34/104.36
active(s(z0)) → s(active(z0)) 334.34/104.36
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.36
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.36
active(dbl(z0)) → dbl(active(z0)) 334.34/104.36
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.36
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.36
terms(mark(z0)) → mark(terms(z0)) 334.34/104.36
terms(ok(z0)) → ok(terms(z0)) 334.34/104.36
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.36
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.36
recip(mark(z0)) → mark(recip(z0)) 334.34/104.36
recip(ok(z0)) → ok(recip(z0)) 334.34/104.36
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.36
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.36
s(mark(z0)) → mark(s(z0)) 334.34/104.36
s(ok(z0)) → ok(s(z0)) 334.34/104.36
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.36
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.36
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.36
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.36
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.36
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.36
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.36
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.36
proper(terms(z0)) → terms(proper(z0)) 334.34/104.36
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.36
proper(recip(z0)) → recip(proper(z0)) 334.34/104.36
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.36
proper(s(z0)) → s(proper(z0)) 334.34/104.36
proper(0) → ok(0) 334.34/104.36
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.36
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.36
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.36
proper(nil) → ok(nil) 334.34/104.36
top(mark(z0)) → top(proper(z0)) 334.34/104.36
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.36
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.36
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.36
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.36
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.36
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.36
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.36
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.36
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.36
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.36
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.36
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.36
S(mark(z0)) → c27(S(z0)) 334.34/104.36
S(ok(z0)) → c28(S(z0)) 334.34/104.36
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.36
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.36
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.36
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.36
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.36
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.36
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.36
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.36
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.36
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.36
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.36
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.36
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.36
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.36
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.36
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.36
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.36
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.36
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.36
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)))) 334.34/104.36
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.36
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.36
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.36
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.36
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.36
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.36
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.36
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.36
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.36
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.36
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.36
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.36
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.34/104.36
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 334.34/104.36
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 334.34/104.36
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.36
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.36
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.36
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.36
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.36
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.36
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.36
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.36
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.36
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.36
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.36
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.36
S(mark(z0)) → c27(S(z0)) 334.34/104.36
S(ok(z0)) → c28(S(z0)) 334.34/104.36
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.36
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.36
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.36
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.36
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.36
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.36
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.36
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.36
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.36
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.36
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.36
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.36
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.36
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.36
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.36
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.36
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.36
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.36
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.36
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)))) 334.34/104.36
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.36
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.36
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.36
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.36
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.36
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.36
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.36
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.36
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.36
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.36
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.36
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.36
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.34/104.36
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 334.34/104.36
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 334.34/104.36
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40, c41, c41, c43

334.34/104.36

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

Removed 4 trailing tuple parts

334.34/104.36

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.36
active(sqr(0)) → mark(0) 334.34/104.36
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.36
active(dbl(0)) → mark(0) 334.34/104.36
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.36
active(add(0, z0)) → mark(z0) 334.34/104.36
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.36
active(first(0, z0)) → mark(nil) 334.34/104.36
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.36
active(terms(z0)) → terms(active(z0)) 334.34/104.36
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.36
active(recip(z0)) → recip(active(z0)) 334.34/104.36
active(sqr(z0)) → sqr(active(z0)) 334.34/104.36
active(s(z0)) → s(active(z0)) 334.34/104.36
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.36
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.36
active(dbl(z0)) → dbl(active(z0)) 334.34/104.36
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.36
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.36
terms(mark(z0)) → mark(terms(z0)) 334.34/104.36
terms(ok(z0)) → ok(terms(z0)) 334.34/104.36
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.36
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.36
recip(mark(z0)) → mark(recip(z0)) 334.34/104.36
recip(ok(z0)) → ok(recip(z0)) 334.34/104.36
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.36
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.36
s(mark(z0)) → mark(s(z0)) 334.34/104.36
s(ok(z0)) → ok(s(z0)) 334.34/104.36
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.36
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.36
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.36
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.36
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.36
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.36
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.36
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.36
proper(terms(z0)) → terms(proper(z0)) 334.34/104.36
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.36
proper(recip(z0)) → recip(proper(z0)) 334.34/104.36
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.36
proper(s(z0)) → s(proper(z0)) 334.34/104.36
proper(0) → ok(0) 334.34/104.36
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.36
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.36
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.36
proper(nil) → ok(nil) 334.34/104.36
top(mark(z0)) → top(proper(z0)) 334.34/104.36
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.36
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.36
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.36
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.36
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.36
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.36
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.36
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.36
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.36
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.36
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.36
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.36
S(mark(z0)) → c27(S(z0)) 334.34/104.36
S(ok(z0)) → c28(S(z0)) 334.34/104.36
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.36
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.36
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.36
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.36
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.36
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.36
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.36
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.36
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.36
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.36
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.36
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.36
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.36
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.36
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.36
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.36
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.36
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.36
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.36
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)))) 334.34/104.36
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.36
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.36
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.36
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.36
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.36
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.36
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.36
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.36
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.36
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.36
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.36
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.36
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.36
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.36
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.36
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.36
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.36
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.36
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.36
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.36
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.36
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.36
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.36
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.36
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.36
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.36
S(mark(z0)) → c27(S(z0)) 334.34/104.36
S(ok(z0)) → c28(S(z0)) 334.34/104.36
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.36
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.36
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.36
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.36
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.36
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.36
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.36
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.36
PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) 334.34/104.36
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.36
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.36
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.36
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.36
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.36
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.36
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.36
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.36
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.36
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.36
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)))) 334.34/104.36
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.36
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.36
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.36
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.36
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.36
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.36
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.36
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.36
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.36
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.36
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.36
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.36
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.36
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.36
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c44, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40, c41, c41, c43, c43

334.34/104.36

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

Use narrowing to replace PROPER(dbl(z0)) → c44(DBL(proper(z0)), PROPER(z0)) by

PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(dbl(0)) → c44(DBL(ok(0)), PROPER(0)) 334.34/104.36
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(dbl(nil)) → c44(DBL(ok(nil)), PROPER(nil))

334.34/104.36

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.36
active(sqr(0)) → mark(0) 334.34/104.36
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.36
active(dbl(0)) → mark(0) 334.34/104.36
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.36
active(add(0, z0)) → mark(z0) 334.34/104.36
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.36
active(first(0, z0)) → mark(nil) 334.34/104.36
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.36
active(terms(z0)) → terms(active(z0)) 334.34/104.36
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.36
active(recip(z0)) → recip(active(z0)) 334.34/104.36
active(sqr(z0)) → sqr(active(z0)) 334.34/104.36
active(s(z0)) → s(active(z0)) 334.34/104.36
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.36
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.36
active(dbl(z0)) → dbl(active(z0)) 334.34/104.36
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.36
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.36
terms(mark(z0)) → mark(terms(z0)) 334.34/104.36
terms(ok(z0)) → ok(terms(z0)) 334.34/104.36
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.36
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.36
recip(mark(z0)) → mark(recip(z0)) 334.34/104.36
recip(ok(z0)) → ok(recip(z0)) 334.34/104.36
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.36
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.36
s(mark(z0)) → mark(s(z0)) 334.34/104.36
s(ok(z0)) → ok(s(z0)) 334.34/104.36
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.36
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.36
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.36
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.36
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.36
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.36
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.36
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.36
proper(terms(z0)) → terms(proper(z0)) 334.34/104.36
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.36
proper(recip(z0)) → recip(proper(z0)) 334.34/104.36
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.36
proper(s(z0)) → s(proper(z0)) 334.34/104.36
proper(0) → ok(0) 334.34/104.36
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.36
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.36
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.36
proper(nil) → ok(nil) 334.34/104.36
top(mark(z0)) → top(proper(z0)) 334.34/104.36
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.36
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.36
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.36
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.36
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.36
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.36
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.36
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.36
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.36
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.36
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.36
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.36
S(mark(z0)) → c27(S(z0)) 334.34/104.36
S(ok(z0)) → c28(S(z0)) 334.34/104.36
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.36
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.36
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.36
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.36
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.36
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.36
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.36
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.36
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.36
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.36
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.36
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.36
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.36
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.36
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.36
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.36
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.36
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.36
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.36
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)))) 334.34/104.36
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.36
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.36
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.36
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.36
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.36
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.36
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.36
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.36
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.36
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.36
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.36
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.36
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.36
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.36
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.36
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.36
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.36
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.36
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.36
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.36
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.36
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.36
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.36
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.36
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.36
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.36
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.36
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.36
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.36
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.36
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.36
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.36
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.36
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.36
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.36
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.36
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.36
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.36
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.36
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.36
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.36
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.36
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.36
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.36
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.36
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.36
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.36
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.36
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.37
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.37
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(dbl(0)) → c44(DBL(ok(0)), PROPER(0)) 334.34/104.37
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(dbl(nil)) → c44(DBL(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.37
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.37
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.37
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.37
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.37
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.37
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.37
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.37
S(mark(z0)) → c27(S(z0)) 334.34/104.37
S(ok(z0)) → c28(S(z0)) 334.34/104.37
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.37
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.37
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.37
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.37
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.37
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.37
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.37
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.37
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.37
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.37
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.37
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.37
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.37
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.37
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.37
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)))) 334.34/104.37
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.37
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.37
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.37
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.37
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.37
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.37
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.37
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.37
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.37
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.37
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.37
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.37
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.37
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.37
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.37
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.37
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.37
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.37
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.37
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.37
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.37
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.37
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.37
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.37
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(dbl(0)) → c44(DBL(ok(0)), PROPER(0)) 334.34/104.37
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(dbl(nil)) → c44(DBL(ok(nil)), PROPER(nil))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40, c41, c41, c43, c43, c44

334.34/104.37

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

Removed 2 trailing tuple parts

334.34/104.37

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.37
active(sqr(0)) → mark(0) 334.34/104.37
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.37
active(dbl(0)) → mark(0) 334.34/104.37
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.37
active(add(0, z0)) → mark(z0) 334.34/104.37
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.37
active(first(0, z0)) → mark(nil) 334.34/104.37
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.37
active(terms(z0)) → terms(active(z0)) 334.34/104.37
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.37
active(recip(z0)) → recip(active(z0)) 334.34/104.37
active(sqr(z0)) → sqr(active(z0)) 334.34/104.37
active(s(z0)) → s(active(z0)) 334.34/104.37
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.37
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.37
active(dbl(z0)) → dbl(active(z0)) 334.34/104.37
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.37
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.37
terms(mark(z0)) → mark(terms(z0)) 334.34/104.37
terms(ok(z0)) → ok(terms(z0)) 334.34/104.37
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.37
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.37
recip(mark(z0)) → mark(recip(z0)) 334.34/104.37
recip(ok(z0)) → ok(recip(z0)) 334.34/104.37
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.37
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.37
s(mark(z0)) → mark(s(z0)) 334.34/104.37
s(ok(z0)) → ok(s(z0)) 334.34/104.37
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.37
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.37
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.37
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.37
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.37
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.37
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.37
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.37
proper(terms(z0)) → terms(proper(z0)) 334.34/104.37
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.37
proper(recip(z0)) → recip(proper(z0)) 334.34/104.37
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.37
proper(s(z0)) → s(proper(z0)) 334.34/104.37
proper(0) → ok(0) 334.34/104.37
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.37
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.37
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.37
proper(nil) → ok(nil) 334.34/104.37
top(mark(z0)) → top(proper(z0)) 334.34/104.37
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.37
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.37
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.37
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.37
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.37
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.37
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.37
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.37
S(mark(z0)) → c27(S(z0)) 334.34/104.37
S(ok(z0)) → c28(S(z0)) 334.34/104.37
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.37
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.37
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.37
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.37
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.37
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.37
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.37
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.37
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.37
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.37
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.37
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.37
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.37
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.37
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.37
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)))) 334.34/104.37
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.37
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.37
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.37
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.37
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.37
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.37
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.37
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.37
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.37
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.37
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.37
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.37
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.37
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.37
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.37
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.37
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.37
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.37
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.37
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.37
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.37
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.37
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.37
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.37
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.37
PROPER(dbl(nil)) → c44(DBL(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.37
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.37
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.37
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.37
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.37
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.37
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.37
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.37
S(mark(z0)) → c27(S(z0)) 334.34/104.37
S(ok(z0)) → c28(S(z0)) 334.34/104.37
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.37
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.37
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.37
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.37
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.37
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.37
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.37
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.37
PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 334.34/104.37
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.37
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.37
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.37
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.37
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.37
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.37
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)))) 334.34/104.37
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.37
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.37
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.37
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.37
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.37
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.37
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.37
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.37
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.37
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.37
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.37
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.37
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.37
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.37
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.37
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.37
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.37
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.37
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.37
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.37
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.37
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.37
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.37
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.37
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.37
PROPER(dbl(nil)) → c44(DBL(ok(nil)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c45, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40, c41, c41, c43, c43, c44, c44

334.34/104.37

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

Use narrowing to replace PROPER(first(z0, z1)) → c45(FIRST(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.34/104.37
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 334.34/104.37
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 334.34/104.37
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

334.34/104.37

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.37
active(sqr(0)) → mark(0) 334.34/104.37
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.37
active(dbl(0)) → mark(0) 334.34/104.37
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.37
active(add(0, z0)) → mark(z0) 334.34/104.37
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.37
active(first(0, z0)) → mark(nil) 334.34/104.37
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.37
active(terms(z0)) → terms(active(z0)) 334.34/104.37
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.37
active(recip(z0)) → recip(active(z0)) 334.34/104.37
active(sqr(z0)) → sqr(active(z0)) 334.34/104.37
active(s(z0)) → s(active(z0)) 334.34/104.37
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.37
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.37
active(dbl(z0)) → dbl(active(z0)) 334.34/104.37
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.37
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.37
terms(mark(z0)) → mark(terms(z0)) 334.34/104.37
terms(ok(z0)) → ok(terms(z0)) 334.34/104.37
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.37
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.37
recip(mark(z0)) → mark(recip(z0)) 334.34/104.37
recip(ok(z0)) → ok(recip(z0)) 334.34/104.37
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.37
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.37
s(mark(z0)) → mark(s(z0)) 334.34/104.37
s(ok(z0)) → ok(s(z0)) 334.34/104.37
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.37
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.37
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.37
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.37
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.37
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.37
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.37
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.37
proper(terms(z0)) → terms(proper(z0)) 334.34/104.37
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.37
proper(recip(z0)) → recip(proper(z0)) 334.34/104.37
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.37
proper(s(z0)) → s(proper(z0)) 334.34/104.37
proper(0) → ok(0) 334.34/104.37
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.37
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.37
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.37
proper(nil) → ok(nil) 334.34/104.37
top(mark(z0)) → top(proper(z0)) 334.34/104.37
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.37
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.37
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.37
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.37
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.37
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.37
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.37
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.37
S(mark(z0)) → c27(S(z0)) 334.34/104.37
S(ok(z0)) → c28(S(z0)) 334.34/104.37
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.37
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.37
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.37
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.37
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.37
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.37
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.37
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.37
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.37
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.37
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.37
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.37
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.37
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.37
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)))) 334.34/104.37
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.37
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.37
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.37
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.37
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.37
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.37
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.37
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.37
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.37
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.37
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.37
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.37
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.37
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.37
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.37
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.37
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.37
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.37
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.37
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.37
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.37
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.37
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.37
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.37
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.37
PROPER(dbl(nil)) → c44(DBL(ok(nil))) 334.34/104.37
PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.34/104.37
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 334.34/104.37
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 334.34/104.37
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.37
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.37
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.37
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.37
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.37
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.37
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.37
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.37
S(mark(z0)) → c27(S(z0)) 334.34/104.37
S(ok(z0)) → c28(S(z0)) 334.34/104.37
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.37
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.37
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.37
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.37
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.37
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.37
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.37
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.37
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.37
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.37
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.37
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.37
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.37
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.37
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)))) 334.34/104.37
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.37
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.37
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.37
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.37
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.37
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.37
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.37
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.37
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.37
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.37
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.37
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.37
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.37
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.37
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.37
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.37
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.37
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.37
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.37
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.37
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.37
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.37
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.37
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.37
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.37
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.37
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.37
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.37
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.37
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.37
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.37
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.37
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.37
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.37
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.37
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.37
PROPER(dbl(nil)) → c44(DBL(ok(nil))) 334.34/104.37
PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.37
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.37
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.37
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.37
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.37
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 334.34/104.37
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.37
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.37
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.37
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0), PROPER(nil)) 334.34/104.37
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 334.34/104.37
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.37
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.37
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(nil), PROPER(x1))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40, c41, c41, c43, c43, c44, c44, c45

334.34/104.37

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

Removed 4 trailing tuple parts

334.34/104.37

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.37
active(sqr(0)) → mark(0) 334.34/104.37
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.37
active(dbl(0)) → mark(0) 334.34/104.37
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.37
active(add(0, z0)) → mark(z0) 334.34/104.37
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.37
active(first(0, z0)) → mark(nil) 334.34/104.37
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.37
active(terms(z0)) → terms(active(z0)) 334.34/104.37
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.37
active(recip(z0)) → recip(active(z0)) 334.34/104.37
active(sqr(z0)) → sqr(active(z0)) 334.34/104.37
active(s(z0)) → s(active(z0)) 334.34/104.37
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.37
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.37
active(dbl(z0)) → dbl(active(z0)) 334.34/104.37
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.37
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.37
terms(mark(z0)) → mark(terms(z0)) 334.34/104.37
terms(ok(z0)) → ok(terms(z0)) 334.34/104.37
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.37
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.37
recip(mark(z0)) → mark(recip(z0)) 334.34/104.37
recip(ok(z0)) → ok(recip(z0)) 334.34/104.37
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.37
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.37
s(mark(z0)) → mark(s(z0)) 334.34/104.37
s(ok(z0)) → ok(s(z0)) 334.34/104.37
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.37
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.37
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.37
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.37
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.37
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.37
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.37
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.37
proper(terms(z0)) → terms(proper(z0)) 334.34/104.37
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.37
proper(recip(z0)) → recip(proper(z0)) 334.34/104.37
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.37
proper(s(z0)) → s(proper(z0)) 334.34/104.37
proper(0) → ok(0) 334.34/104.37
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.37
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.37
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.37
proper(nil) → ok(nil) 334.34/104.37
top(mark(z0)) → top(proper(z0)) 334.34/104.37
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.37
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.37
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.37
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.37
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.37
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.37
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.37
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.37
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.37
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.37
S(mark(z0)) → c27(S(z0)) 334.34/104.37
S(ok(z0)) → c28(S(z0)) 334.34/104.37
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.37
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.37
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.37
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.37
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.37
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.37
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.37
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.37
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.37
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.37
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.37
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.37
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.37
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.37
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.37
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.37
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.37
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.37
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.37
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.37
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.37
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.37
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.37
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.37
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.37
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.37
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.38
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)))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.38
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.38
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.38
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.38
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.38
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.38
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.38
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.38
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.38
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.38
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.38
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.38
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.38
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.38
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.38
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.38
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.38
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.38
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.38
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.38
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.38
PROPER(dbl(nil)) → c44(DBL(ok(nil))) 334.34/104.38
PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.38
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.38
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.38
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.38
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.38
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.38
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.38
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.38
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.38
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.38
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.38
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.38
S(mark(z0)) → c27(S(z0)) 334.34/104.38
S(ok(z0)) → c28(S(z0)) 334.34/104.38
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.38
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.38
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.38
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.38
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.38
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.38
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.38
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.38
TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) 334.34/104.38
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.38
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.38
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.38
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.38
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.38
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.38
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.38
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.38
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)))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.38
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.38
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.38
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.38
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.38
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.38
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.38
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.38
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.38
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.38
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.38
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.38
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.38
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.38
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.38
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.38
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.38
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.38
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.38
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.38
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.38
PROPER(dbl(nil)) → c44(DBL(ok(nil))) 334.34/104.38
PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c47, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40, c41, c41, c43, c43, c44, c44, c45, c45

334.34/104.38

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

Use narrowing to replace TOP(mark(z0)) → c47(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(terms(z0))) → c47(TOP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
TOP(mark(cons(z0, z1))) → c47(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
TOP(mark(recip(z0))) → c47(TOP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
TOP(mark(sqr(z0))) → c47(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
TOP(mark(s(z0))) → c47(TOP(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
TOP(mark(0)) → c47(TOP(ok(0)), PROPER(0)) 334.34/104.38
TOP(mark(add(z0, z1))) → c47(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
TOP(mark(dbl(z0))) → c47(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
TOP(mark(first(z0, z1))) → c47(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
TOP(mark(nil)) → c47(TOP(ok(nil)), PROPER(nil))

334.34/104.38

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.38
active(sqr(0)) → mark(0) 334.34/104.38
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.38
active(dbl(0)) → mark(0) 334.34/104.38
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.38
active(add(0, z0)) → mark(z0) 334.34/104.38
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.38
active(first(0, z0)) → mark(nil) 334.34/104.38
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.38
active(terms(z0)) → terms(active(z0)) 334.34/104.38
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.38
active(recip(z0)) → recip(active(z0)) 334.34/104.38
active(sqr(z0)) → sqr(active(z0)) 334.34/104.38
active(s(z0)) → s(active(z0)) 334.34/104.38
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.38
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.38
active(dbl(z0)) → dbl(active(z0)) 334.34/104.38
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.38
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.38
terms(mark(z0)) → mark(terms(z0)) 334.34/104.38
terms(ok(z0)) → ok(terms(z0)) 334.34/104.38
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.38
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.38
recip(mark(z0)) → mark(recip(z0)) 334.34/104.38
recip(ok(z0)) → ok(recip(z0)) 334.34/104.38
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.38
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.38
s(mark(z0)) → mark(s(z0)) 334.34/104.38
s(ok(z0)) → ok(s(z0)) 334.34/104.38
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.38
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.38
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.38
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.38
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.38
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.38
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.38
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.38
proper(terms(z0)) → terms(proper(z0)) 334.34/104.38
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.38
proper(recip(z0)) → recip(proper(z0)) 334.34/104.38
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.38
proper(s(z0)) → s(proper(z0)) 334.34/104.38
proper(0) → ok(0) 334.34/104.38
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.38
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.38
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.38
proper(nil) → ok(nil) 334.34/104.38
top(mark(z0)) → top(proper(z0)) 334.34/104.38
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.38
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.38
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.38
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.38
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.38
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.38
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.38
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.38
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.38
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.38
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.38
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.38
S(mark(z0)) → c27(S(z0)) 334.34/104.38
S(ok(z0)) → c28(S(z0)) 334.34/104.38
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.38
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.38
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.38
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.38
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.38
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.38
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.38
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.38
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.38
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.38
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.38
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.38
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.38
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.38
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.38
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.38
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)))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.38
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.38
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.38
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.38
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.38
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.38
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.38
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.38
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.38
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.38
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.38
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.38
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.38
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.38
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.38
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.38
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.38
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.38
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.38
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.38
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.38
PROPER(dbl(nil)) → c44(DBL(ok(nil))) 334.34/104.38
PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
TOP(mark(terms(z0))) → c47(TOP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
TOP(mark(cons(z0, z1))) → c47(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
TOP(mark(recip(z0))) → c47(TOP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
TOP(mark(sqr(z0))) → c47(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
TOP(mark(s(z0))) → c47(TOP(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
TOP(mark(0)) → c47(TOP(ok(0)), PROPER(0)) 334.34/104.38
TOP(mark(add(z0, z1))) → c47(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
TOP(mark(dbl(z0))) → c47(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
TOP(mark(first(z0, z1))) → c47(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
TOP(mark(nil)) → c47(TOP(ok(nil)), PROPER(nil))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.38
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.38
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.38
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.38
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.38
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.38
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.38
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.38
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.38
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.38
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.38
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.38
S(mark(z0)) → c27(S(z0)) 334.34/104.38
S(ok(z0)) → c28(S(z0)) 334.34/104.38
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.38
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.38
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.38
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.38
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.38
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.38
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.38
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.38
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.38
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.38
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.38
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.38
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.38
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.38
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.38
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.38
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)))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.38
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.38
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.38
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.38
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.38
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.38
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.38
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.38
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.38
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.38
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.38
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.38
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.38
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.38
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.38
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.38
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.38
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.38
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.38
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.38
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.38
PROPER(dbl(nil)) → c44(DBL(ok(nil))) 334.34/104.38
PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
TOP(mark(terms(z0))) → c47(TOP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
TOP(mark(cons(z0, z1))) → c47(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
TOP(mark(recip(z0))) → c47(TOP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
TOP(mark(sqr(z0))) → c47(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
TOP(mark(s(z0))) → c47(TOP(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
TOP(mark(0)) → c47(TOP(ok(0)), PROPER(0)) 334.34/104.38
TOP(mark(add(z0, z1))) → c47(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
TOP(mark(dbl(z0))) → c47(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
TOP(mark(first(z0, z1))) → c47(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
TOP(mark(nil)) → c47(TOP(ok(nil)), PROPER(nil))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40, c41, c41, c43, c43, c44, c44, c45, c45, c47

334.34/104.38

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

Removed 2 trailing tuple parts

334.34/104.38

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.38
active(sqr(0)) → mark(0) 334.34/104.38
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.38
active(dbl(0)) → mark(0) 334.34/104.38
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.38
active(add(0, z0)) → mark(z0) 334.34/104.38
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.38
active(first(0, z0)) → mark(nil) 334.34/104.38
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.38
active(terms(z0)) → terms(active(z0)) 334.34/104.38
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.38
active(recip(z0)) → recip(active(z0)) 334.34/104.38
active(sqr(z0)) → sqr(active(z0)) 334.34/104.38
active(s(z0)) → s(active(z0)) 334.34/104.38
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.38
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.38
active(dbl(z0)) → dbl(active(z0)) 334.34/104.38
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.38
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.38
terms(mark(z0)) → mark(terms(z0)) 334.34/104.38
terms(ok(z0)) → ok(terms(z0)) 334.34/104.38
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.38
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.38
recip(mark(z0)) → mark(recip(z0)) 334.34/104.38
recip(ok(z0)) → ok(recip(z0)) 334.34/104.38
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.38
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.38
s(mark(z0)) → mark(s(z0)) 334.34/104.38
s(ok(z0)) → ok(s(z0)) 334.34/104.38
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.38
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.38
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.38
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.38
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.38
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.38
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.38
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.38
proper(terms(z0)) → terms(proper(z0)) 334.34/104.38
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.38
proper(recip(z0)) → recip(proper(z0)) 334.34/104.38
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.38
proper(s(z0)) → s(proper(z0)) 334.34/104.38
proper(0) → ok(0) 334.34/104.38
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.38
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.38
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.38
proper(nil) → ok(nil) 334.34/104.38
top(mark(z0)) → top(proper(z0)) 334.34/104.38
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.38
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.38
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.38
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.38
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.38
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.38
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.38
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.38
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.38
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.38
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.38
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.38
S(mark(z0)) → c27(S(z0)) 334.34/104.38
S(ok(z0)) → c28(S(z0)) 334.34/104.38
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.38
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.38
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.38
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.38
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.38
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.38
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.38
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.38
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.38
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.38
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.38
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.38
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.38
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.38
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.38
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.38
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)))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.38
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.38
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.38
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.38
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.38
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.38
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.38
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.38
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.38
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.38
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.38
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.38
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.38
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.38
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.38
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.38
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.38
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.38
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.38
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.38
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.38
PROPER(dbl(nil)) → c44(DBL(ok(nil))) 334.34/104.38
PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.38
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.38
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.38
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.38
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.38
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.38
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.38
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.38
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.38
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.38
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0)) 334.34/104.38
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.38
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(x1)) 334.34/104.38
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.38
TOP(mark(terms(z0))) → c47(TOP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.38
TOP(mark(cons(z0, z1))) → c47(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.38
TOP(mark(recip(z0))) → c47(TOP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.38
TOP(mark(sqr(z0))) → c47(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.38
TOP(mark(s(z0))) → c47(TOP(s(proper(z0))), PROPER(s(z0))) 334.34/104.38
TOP(mark(add(z0, z1))) → c47(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.38
TOP(mark(dbl(z0))) → c47(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.38
TOP(mark(first(z0, z1))) → c47(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.38
TOP(mark(0)) → c47(TOP(ok(0))) 334.34/104.38
TOP(mark(nil)) → c47(TOP(ok(nil)))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.38
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.38
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.38
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.38
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.38
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.38
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.38
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.38
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.38
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.38
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.38
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.38
S(mark(z0)) → c27(S(z0)) 334.34/104.38
S(ok(z0)) → c28(S(z0)) 334.34/104.38
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.38
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.38
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.38
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.38
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.38
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.38
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.38
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.38
TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) 334.34/104.38
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.38
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.38
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.38
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.38
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.38
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.38
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.38
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.38
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)))) 334.34/104.38
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.38
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.38
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.38
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.38
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.38
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.38
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.38
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.38
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.38
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.38
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.38
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.39
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.39
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.39
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.39
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.39
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.39
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.39
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.39
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.39
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.39
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.39
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.39
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.39
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.39
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.39
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.39
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.39
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.39
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.39
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.39
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.39
PROPER(dbl(nil)) → c44(DBL(ok(nil))) 334.34/104.39
PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
TOP(mark(terms(z0))) → c47(TOP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
TOP(mark(cons(z0, z1))) → c47(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
TOP(mark(recip(z0))) → c47(TOP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
TOP(mark(sqr(z0))) → c47(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
TOP(mark(s(z0))) → c47(TOP(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
TOP(mark(add(z0, z1))) → c47(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
TOP(mark(dbl(z0))) → c47(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
TOP(mark(first(z0, z1))) → c47(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
TOP(mark(0)) → c47(TOP(ok(0))) 334.34/104.39
TOP(mark(nil)) → c47(TOP(ok(nil)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40, c41, c41, c43, c43, c44, c44, c45, c45, c47, c47

334.34/104.39

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

Use narrowing to replace TOP(ok(z0)) → c48(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(terms(z0))) → c48(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
TOP(ok(sqr(0))) → c48(TOP(mark(0)), ACTIVE(sqr(0))) 334.34/104.39
TOP(ok(sqr(s(z0)))) → c48(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
TOP(ok(dbl(0))) → c48(TOP(mark(0)), ACTIVE(dbl(0))) 334.34/104.39
TOP(ok(dbl(s(z0)))) → c48(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
TOP(ok(add(0, z0))) → c48(TOP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
TOP(ok(add(s(z0), z1))) → c48(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
TOP(ok(first(0, z0))) → c48(TOP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
TOP(ok(first(s(z0), cons(z1, z2)))) → c48(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
TOP(ok(terms(z0))) → c48(TOP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
TOP(ok(cons(z0, z1))) → c48(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
TOP(ok(recip(z0))) → c48(TOP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
TOP(ok(sqr(z0))) → c48(TOP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
TOP(ok(s(z0))) → c48(TOP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
TOP(ok(add(z0, z1))) → c48(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
TOP(ok(add(z0, z1))) → c48(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
TOP(ok(dbl(z0))) → c48(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
TOP(ok(first(z0, z1))) → c48(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
TOP(ok(first(z0, z1))) → c48(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

334.34/104.39

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.39
active(sqr(0)) → mark(0) 334.34/104.39
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.39
active(dbl(0)) → mark(0) 334.34/104.39
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.39
active(add(0, z0)) → mark(z0) 334.34/104.39
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.39
active(first(0, z0)) → mark(nil) 334.34/104.39
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.39
active(terms(z0)) → terms(active(z0)) 334.34/104.39
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.39
active(recip(z0)) → recip(active(z0)) 334.34/104.39
active(sqr(z0)) → sqr(active(z0)) 334.34/104.39
active(s(z0)) → s(active(z0)) 334.34/104.39
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.39
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.39
active(dbl(z0)) → dbl(active(z0)) 334.34/104.39
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.39
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.39
terms(mark(z0)) → mark(terms(z0)) 334.34/104.39
terms(ok(z0)) → ok(terms(z0)) 334.34/104.39
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.39
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.39
recip(mark(z0)) → mark(recip(z0)) 334.34/104.39
recip(ok(z0)) → ok(recip(z0)) 334.34/104.39
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.39
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.39
s(mark(z0)) → mark(s(z0)) 334.34/104.39
s(ok(z0)) → ok(s(z0)) 334.34/104.39
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.39
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.39
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.39
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.39
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.39
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.39
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.39
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.39
proper(terms(z0)) → terms(proper(z0)) 334.34/104.39
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.39
proper(recip(z0)) → recip(proper(z0)) 334.34/104.39
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.39
proper(s(z0)) → s(proper(z0)) 334.34/104.39
proper(0) → ok(0) 334.34/104.39
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.39
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.39
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.39
proper(nil) → ok(nil) 334.34/104.39
top(mark(z0)) → top(proper(z0)) 334.34/104.39
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.39
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.39
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.39
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.39
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.39
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.39
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.39
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.39
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.39
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.39
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.39
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.39
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)))) 334.34/104.39
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.39
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.39
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.39
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.39
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.39
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.39
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.39
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.39
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.39
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.39
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.39
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.39
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.39
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.39
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.39
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.39
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.39
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.39
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.39
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.39
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.39
PROPER(dbl(nil)) → c44(DBL(ok(nil))) 334.34/104.39
PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
TOP(mark(terms(z0))) → c47(TOP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
TOP(mark(cons(z0, z1))) → c47(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
TOP(mark(recip(z0))) → c47(TOP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
TOP(mark(sqr(z0))) → c47(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
TOP(mark(s(z0))) → c47(TOP(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
TOP(mark(add(z0, z1))) → c47(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
TOP(mark(dbl(z0))) → c47(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
TOP(mark(first(z0, z1))) → c47(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
TOP(mark(0)) → c47(TOP(ok(0))) 334.34/104.39
TOP(mark(nil)) → c47(TOP(ok(nil))) 334.34/104.39
TOP(ok(terms(z0))) → c48(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
TOP(ok(sqr(0))) → c48(TOP(mark(0)), ACTIVE(sqr(0))) 334.34/104.39
TOP(ok(sqr(s(z0)))) → c48(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
TOP(ok(dbl(0))) → c48(TOP(mark(0)), ACTIVE(dbl(0))) 334.34/104.39
TOP(ok(dbl(s(z0)))) → c48(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
TOP(ok(add(0, z0))) → c48(TOP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
TOP(ok(add(s(z0), z1))) → c48(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
TOP(ok(first(0, z0))) → c48(TOP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
TOP(ok(first(s(z0), cons(z1, z2)))) → c48(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
TOP(ok(terms(z0))) → c48(TOP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
TOP(ok(cons(z0, z1))) → c48(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
TOP(ok(recip(z0))) → c48(TOP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
TOP(ok(sqr(z0))) → c48(TOP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
TOP(ok(s(z0))) → c48(TOP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
TOP(ok(add(z0, z1))) → c48(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
TOP(ok(add(z0, z1))) → c48(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
TOP(ok(dbl(z0))) → c48(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
TOP(ok(first(z0, z1))) → c48(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
TOP(ok(first(z0, z1))) → c48(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

S tuples:

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.39
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.39
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.39
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.39
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.39
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.39
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.39
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.39
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.39
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.39
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.39
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.39
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)))) 334.34/104.39
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.39
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.39
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.39
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.39
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.39
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.39
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.39
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.39
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.39
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.39
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.39
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.39
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.39
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.39
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.39
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.39
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.39
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.39
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.39
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.39
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.39
PROPER(dbl(nil)) → c44(DBL(ok(nil))) 334.34/104.39
PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
TOP(mark(terms(z0))) → c47(TOP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
TOP(mark(cons(z0, z1))) → c47(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
TOP(mark(recip(z0))) → c47(TOP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
TOP(mark(sqr(z0))) → c47(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
TOP(mark(s(z0))) → c47(TOP(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
TOP(mark(add(z0, z1))) → c47(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
TOP(mark(dbl(z0))) → c47(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
TOP(mark(first(z0, z1))) → c47(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
TOP(mark(0)) → c47(TOP(ok(0))) 334.34/104.39
TOP(mark(nil)) → c47(TOP(ok(nil))) 334.34/104.39
TOP(ok(terms(z0))) → c48(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
TOP(ok(sqr(0))) → c48(TOP(mark(0)), ACTIVE(sqr(0))) 334.34/104.39
TOP(ok(sqr(s(z0)))) → c48(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
TOP(ok(dbl(0))) → c48(TOP(mark(0)), ACTIVE(dbl(0))) 334.34/104.39
TOP(ok(dbl(s(z0)))) → c48(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
TOP(ok(add(0, z0))) → c48(TOP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
TOP(ok(add(s(z0), z1))) → c48(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
TOP(ok(first(0, z0))) → c48(TOP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
TOP(ok(first(s(z0), cons(z1, z2)))) → c48(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
TOP(ok(terms(z0))) → c48(TOP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
TOP(ok(cons(z0, z1))) → c48(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
TOP(ok(recip(z0))) → c48(TOP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
TOP(ok(sqr(z0))) → c48(TOP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
TOP(ok(s(z0))) → c48(TOP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
TOP(ok(add(z0, z1))) → c48(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
TOP(ok(add(z0, z1))) → c48(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
TOP(ok(dbl(z0))) → c48(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
TOP(ok(first(z0, z1))) → c48(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
TOP(ok(first(z0, z1))) → c48(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c14, c15, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c4, c6, c1, c9, c10, c11, c12, c9, c10, c11, c12, c13, c13, c16, c16, c37, c37, c38, c38, c39, c39, c40, c40, c41, c41, c43, c43, c44, c44, c45, c45, c47, c47, c48

334.34/104.39

(63) CdtUnreachableProof (EQUIVALENT transformation)

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

ACTIVE(add(z0, z1)) → c14(ADD(active(z0), z1), ACTIVE(z0)) 334.34/104.39
ACTIVE(add(z0, z1)) → c15(ADD(z0, active(z1)), ACTIVE(z1)) 334.34/104.39
ACTIVE(first(z0, z1)) → c17(FIRST(active(z0), z1), ACTIVE(z0)) 334.34/104.39
ACTIVE(first(z0, z1)) → c18(FIRST(z0, active(z1)), ACTIVE(z1)) 334.34/104.39
ACTIVE(dbl(s(z0))) → c4(DBL(z0)) 334.34/104.39
ACTIVE(add(s(z0), z1)) → c6(ADD(z0, z1)) 334.34/104.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(CONS(z1, first(z0, z2))) 334.34/104.39
ACTIVE(first(s(z0), cons(z1, z2))) → c1(FIRST(z0, z2)) 334.34/104.39
ACTIVE(terms(z0)) → c1(SQR(z0)) 334.34/104.39
ACTIVE(terms(z0)) → c1(S(z0)) 334.34/104.39
ACTIVE(sqr(s(z0))) → c1(SQR(z0)) 334.34/104.39
ACTIVE(sqr(s(z0))) → c1(DBL(z0)) 334.34/104.39
ACTIVE(terms(terms(z0))) → c9(TERMS(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(terms(sqr(s(z0)))) → c9(TERMS(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(terms(dbl(s(z0)))) → c9(TERMS(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(terms(add(0, z0))) → c9(TERMS(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(terms(add(s(z0), z1))) → c9(TERMS(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(terms(first(0, z0))) → c9(TERMS(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(terms(first(s(z0), cons(z1, z2)))) → c9(TERMS(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(terms(terms(z0))) → c9(TERMS(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(terms(cons(z0, z1))) → c9(TERMS(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(terms(recip(z0))) → c9(TERMS(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(terms(sqr(z0))) → c9(TERMS(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(terms(s(z0))) → c9(TERMS(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(terms(add(z0, z1))) → c9(TERMS(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(terms(dbl(z0))) → c9(TERMS(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(terms(first(z0, z1))) → c9(TERMS(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(cons(terms(z0), x1)) → c10(CONS(mark(cons(recip(sqr(z0)), terms(s(z0)))), x1), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(cons(sqr(s(z0)), x1)) → c10(CONS(mark(s(add(sqr(z0), dbl(z0)))), x1), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(cons(dbl(s(z0)), x1)) → c10(CONS(mark(s(s(dbl(z0)))), x1), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(cons(add(0, z0), x1)) → c10(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(cons(add(s(z0), z1), x1)) → c10(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(cons(first(0, z0), x1)) → c10(CONS(mark(nil), x1), ACTIVE(first(0, z0))) 334.34/104.39
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)))) 334.34/104.39
ACTIVE(cons(terms(z0), x1)) → c10(CONS(terms(active(z0)), x1), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(cons(cons(z0, z1), x1)) → c10(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(cons(recip(z0), x1)) → c10(CONS(recip(active(z0)), x1), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(cons(sqr(z0), x1)) → c10(CONS(sqr(active(z0)), x1), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(cons(s(z0), x1)) → c10(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(cons(add(z0, z1), x1)) → c10(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(cons(dbl(z0), x1)) → c10(CONS(dbl(active(z0)), x1), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(active(z0), z1), x1), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(cons(first(z0, z1), x1)) → c10(CONS(first(z0, active(z1)), x1), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(recip(terms(z0))) → c11(RECIP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(recip(sqr(s(z0)))) → c11(RECIP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(recip(dbl(s(z0)))) → c11(RECIP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(recip(add(0, z0))) → c11(RECIP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(recip(add(s(z0), z1))) → c11(RECIP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(recip(first(0, z0))) → c11(RECIP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(recip(first(s(z0), cons(z1, z2)))) → c11(RECIP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(recip(terms(z0))) → c11(RECIP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(recip(cons(z0, z1))) → c11(RECIP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(recip(recip(z0))) → c11(RECIP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(recip(sqr(z0))) → c11(RECIP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(recip(s(z0))) → c11(RECIP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(recip(add(z0, z1))) → c11(RECIP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(recip(dbl(z0))) → c11(RECIP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(recip(first(z0, z1))) → c11(RECIP(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(sqr(terms(z0))) → c12(SQR(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(sqr(sqr(s(z0)))) → c12(SQR(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(sqr(dbl(s(z0)))) → c12(SQR(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(sqr(add(0, z0))) → c12(SQR(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(sqr(add(s(z0), z1))) → c12(SQR(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(sqr(first(0, z0))) → c12(SQR(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(sqr(first(s(z0), cons(z1, z2)))) → c12(SQR(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(sqr(terms(z0))) → c12(SQR(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(sqr(cons(z0, z1))) → c12(SQR(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(sqr(recip(z0))) → c12(SQR(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(sqr(sqr(z0))) → c12(SQR(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(sqr(s(z0))) → c12(SQR(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(sqr(add(z0, z1))) → c12(SQR(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(sqr(dbl(z0))) → c12(SQR(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(sqr(first(z0, z1))) → c12(SQR(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(terms(sqr(0))) → c9(TERMS(mark(0))) 334.34/104.39
ACTIVE(cons(sqr(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.39
ACTIVE(recip(sqr(0))) → c11(RECIP(mark(0))) 334.34/104.39
ACTIVE(sqr(sqr(0))) → c12(SQR(mark(0))) 334.34/104.39
ACTIVE(s(terms(z0))) → c13(S(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(s(sqr(s(z0)))) → c13(S(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(s(dbl(s(z0)))) → c13(S(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(s(add(0, z0))) → c13(S(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(s(add(s(z0), z1))) → c13(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(s(first(0, z0))) → c13(S(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(s(first(s(z0), cons(z1, z2)))) → c13(S(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(s(terms(z0))) → c13(S(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(s(cons(z0, z1))) → c13(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(s(recip(z0))) → c13(S(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(s(sqr(z0))) → c13(S(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(s(s(z0))) → c13(S(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(s(add(z0, z1))) → c13(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(s(add(z0, z1))) → c13(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(s(dbl(z0))) → c13(S(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(s(first(z0, z1))) → c13(S(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(s(first(z0, z1))) → c13(S(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(s(sqr(0))) → c13(S(mark(0))) 334.34/104.39
ACTIVE(dbl(terms(z0))) → c16(DBL(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(dbl(sqr(s(z0)))) → c16(DBL(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
ACTIVE(dbl(dbl(s(z0)))) → c16(DBL(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
ACTIVE(dbl(add(0, z0))) → c16(DBL(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
ACTIVE(dbl(add(s(z0), z1))) → c16(DBL(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
ACTIVE(dbl(first(0, z0))) → c16(DBL(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
ACTIVE(dbl(first(s(z0), cons(z1, z2)))) → c16(DBL(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
ACTIVE(dbl(terms(z0))) → c16(DBL(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
ACTIVE(dbl(cons(z0, z1))) → c16(DBL(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
ACTIVE(dbl(recip(z0))) → c16(DBL(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
ACTIVE(dbl(sqr(z0))) → c16(DBL(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
ACTIVE(dbl(s(z0))) → c16(DBL(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(dbl(add(z0, z1))) → c16(DBL(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
ACTIVE(dbl(dbl(z0))) → c16(DBL(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(dbl(first(z0, z1))) → c16(DBL(first(z0, active(z1))), ACTIVE(first(z0, z1))) 334.34/104.39
ACTIVE(terms(dbl(0))) → c9(TERMS(mark(0))) 334.34/104.39
ACTIVE(cons(dbl(0), x1)) → c10(CONS(mark(0), x1)) 334.34/104.39
ACTIVE(recip(dbl(0))) → c11(RECIP(mark(0))) 334.34/104.39
ACTIVE(sqr(dbl(0))) → c12(SQR(mark(0))) 334.34/104.39
ACTIVE(s(dbl(0))) → c13(S(mark(0))) 334.34/104.39
ACTIVE(dbl(sqr(0))) → c16(DBL(mark(0))) 334.34/104.39
ACTIVE(dbl(dbl(0))) → c16(DBL(mark(0))) 334.34/104.39
PROPER(terms(terms(z0))) → c37(TERMS(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(terms(cons(z0, z1))) → c37(TERMS(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(terms(recip(z0))) → c37(TERMS(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(terms(sqr(z0))) → c37(TERMS(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(terms(s(z0))) → c37(TERMS(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(terms(add(z0, z1))) → c37(TERMS(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(terms(dbl(z0))) → c37(TERMS(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(terms(first(z0, z1))) → c37(TERMS(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(terms(0)) → c37(TERMS(ok(0))) 334.34/104.39
PROPER(terms(nil)) → c37(TERMS(ok(nil))) 334.34/104.39
PROPER(cons(x0, terms(z0))) → c38(CONS(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(cons(x0, cons(z0, z1))) → c38(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(cons(x0, recip(z0))) → c38(CONS(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(cons(x0, sqr(z0))) → c38(CONS(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(cons(x0, s(z0))) → c38(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(cons(x0, add(z0, z1))) → c38(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(cons(x0, dbl(z0))) → c38(CONS(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(cons(x0, first(z0, z1))) → c38(CONS(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(cons(terms(z0), x1)) → c38(CONS(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(cons(z0, z1), x1)) → c38(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(recip(z0), x1)) → c38(CONS(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(sqr(z0), x1)) → c38(CONS(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(s(z0), x1)) → c38(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(add(z0, z1), x1)) → c38(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(dbl(z0), x1)) → c38(CONS(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(cons(first(z0, z1), x1)) → c38(CONS(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(cons(x0, 0)) → c38(CONS(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(cons(x0, nil)) → c38(CONS(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(cons(0, x1)) → c38(CONS(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(cons(nil, x1)) → c38(CONS(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(recip(terms(z0))) → c39(RECIP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(recip(cons(z0, z1))) → c39(RECIP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(recip(recip(z0))) → c39(RECIP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(recip(sqr(z0))) → c39(RECIP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(recip(s(z0))) → c39(RECIP(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(recip(add(z0, z1))) → c39(RECIP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(recip(dbl(z0))) → c39(RECIP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(recip(first(z0, z1))) → c39(RECIP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(recip(0)) → c39(RECIP(ok(0))) 334.34/104.39
PROPER(recip(nil)) → c39(RECIP(ok(nil))) 334.34/104.39
PROPER(sqr(terms(z0))) → c40(SQR(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(sqr(cons(z0, z1))) → c40(SQR(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(sqr(recip(z0))) → c40(SQR(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(sqr(sqr(z0))) → c40(SQR(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(sqr(s(z0))) → c40(SQR(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(sqr(add(z0, z1))) → c40(SQR(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(sqr(dbl(z0))) → c40(SQR(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(sqr(first(z0, z1))) → c40(SQR(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(sqr(0)) → c40(SQR(ok(0))) 334.34/104.39
PROPER(sqr(nil)) → c40(SQR(ok(nil))) 334.34/104.39
PROPER(s(terms(z0))) → c41(S(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(s(cons(z0, z1))) → c41(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(s(recip(z0))) → c41(S(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(s(sqr(z0))) → c41(S(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(s(s(z0))) → c41(S(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(s(add(z0, z1))) → c41(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(s(dbl(z0))) → c41(S(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(s(first(z0, z1))) → c41(S(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(s(0)) → c41(S(ok(0))) 334.34/104.39
PROPER(s(nil)) → c41(S(ok(nil))) 334.34/104.39
PROPER(add(x0, terms(z0))) → c43(ADD(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(add(x0, cons(z0, z1))) → c43(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(add(x0, recip(z0))) → c43(ADD(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(add(x0, sqr(z0))) → c43(ADD(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(add(x0, s(z0))) → c43(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(add(x0, add(z0, z1))) → c43(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(add(x0, dbl(z0))) → c43(ADD(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(add(x0, first(z0, z1))) → c43(ADD(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(add(terms(z0), x1)) → c43(ADD(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(cons(z0, z1), x1)) → c43(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(recip(z0), x1)) → c43(ADD(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(sqr(z0), x1)) → c43(ADD(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(s(z0), x1)) → c43(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(add(z0, z1), x1)) → c43(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(dbl(z0), x1)) → c43(ADD(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(add(first(z0, z1), x1)) → c43(ADD(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(add(x0, 0)) → c43(ADD(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(add(x0, nil)) → c43(ADD(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(add(0, x1)) → c43(ADD(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(add(nil, x1)) → c43(ADD(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(dbl(terms(z0))) → c44(DBL(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
PROPER(dbl(cons(z0, z1))) → c44(DBL(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(dbl(recip(z0))) → c44(DBL(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
PROPER(dbl(sqr(z0))) → c44(DBL(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
PROPER(dbl(s(z0))) → c44(DBL(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
PROPER(dbl(add(z0, z1))) → c44(DBL(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
PROPER(dbl(dbl(z0))) → c44(DBL(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
PROPER(dbl(first(z0, z1))) → c44(DBL(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
PROPER(dbl(0)) → c44(DBL(ok(0))) 334.34/104.39
PROPER(dbl(nil)) → c44(DBL(ok(nil))) 334.34/104.39
PROPER(first(x0, terms(z0))) → c45(FIRST(proper(x0), terms(proper(z0))), PROPER(x0), PROPER(terms(z0))) 334.34/104.39
PROPER(first(x0, cons(z0, z1))) → c45(FIRST(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 334.34/104.39
PROPER(first(x0, recip(z0))) → c45(FIRST(proper(x0), recip(proper(z0))), PROPER(x0), PROPER(recip(z0))) 334.34/104.39
PROPER(first(x0, sqr(z0))) → c45(FIRST(proper(x0), sqr(proper(z0))), PROPER(x0), PROPER(sqr(z0))) 334.34/104.39
PROPER(first(x0, s(z0))) → c45(FIRST(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 334.34/104.39
PROPER(first(x0, add(z0, z1))) → c45(FIRST(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 334.34/104.39
PROPER(first(x0, dbl(z0))) → c45(FIRST(proper(x0), dbl(proper(z0))), PROPER(x0), PROPER(dbl(z0))) 334.34/104.39
PROPER(first(x0, first(z0, z1))) → c45(FIRST(proper(x0), first(proper(z0), proper(z1))), PROPER(x0), PROPER(first(z0, z1))) 334.34/104.39
PROPER(first(terms(z0), x1)) → c45(FIRST(terms(proper(z0)), proper(x1)), PROPER(terms(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(cons(z0, z1), x1)) → c45(FIRST(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(recip(z0), x1)) → c45(FIRST(recip(proper(z0)), proper(x1)), PROPER(recip(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(sqr(z0), x1)) → c45(FIRST(sqr(proper(z0)), proper(x1)), PROPER(sqr(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(s(z0), x1)) → c45(FIRST(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(add(z0, z1), x1)) → c45(FIRST(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(dbl(z0), x1)) → c45(FIRST(dbl(proper(z0)), proper(x1)), PROPER(dbl(z0)), PROPER(x1)) 334.34/104.39
PROPER(first(first(z0, z1), x1)) → c45(FIRST(first(proper(z0), proper(z1)), proper(x1)), PROPER(first(z0, z1)), PROPER(x1)) 334.34/104.39
PROPER(first(x0, 0)) → c45(FIRST(proper(x0), ok(0)), PROPER(x0)) 334.34/104.39
PROPER(first(x0, nil)) → c45(FIRST(proper(x0), ok(nil)), PROPER(x0)) 334.34/104.39
PROPER(first(0, x1)) → c45(FIRST(ok(0), proper(x1)), PROPER(x1)) 334.34/104.39
PROPER(first(nil, x1)) → c45(FIRST(ok(nil), proper(x1)), PROPER(x1)) 334.34/104.39
TOP(mark(terms(z0))) → c47(TOP(terms(proper(z0))), PROPER(terms(z0))) 334.34/104.39
TOP(mark(cons(z0, z1))) → c47(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 334.34/104.39
TOP(mark(recip(z0))) → c47(TOP(recip(proper(z0))), PROPER(recip(z0))) 334.34/104.39
TOP(mark(sqr(z0))) → c47(TOP(sqr(proper(z0))), PROPER(sqr(z0))) 334.34/104.39
TOP(mark(s(z0))) → c47(TOP(s(proper(z0))), PROPER(s(z0))) 334.34/104.39
TOP(mark(add(z0, z1))) → c47(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 334.34/104.39
TOP(mark(dbl(z0))) → c47(TOP(dbl(proper(z0))), PROPER(dbl(z0))) 334.34/104.39
TOP(mark(first(z0, z1))) → c47(TOP(first(proper(z0), proper(z1))), PROPER(first(z0, z1))) 334.34/104.39
TOP(ok(terms(z0))) → c48(TOP(mark(cons(recip(sqr(z0)), terms(s(z0))))), ACTIVE(terms(z0))) 334.34/104.39
TOP(ok(sqr(0))) → c48(TOP(mark(0)), ACTIVE(sqr(0))) 334.34/104.39
TOP(ok(sqr(s(z0)))) → c48(TOP(mark(s(add(sqr(z0), dbl(z0))))), ACTIVE(sqr(s(z0)))) 334.34/104.39
TOP(ok(dbl(0))) → c48(TOP(mark(0)), ACTIVE(dbl(0))) 334.34/104.39
TOP(ok(dbl(s(z0)))) → c48(TOP(mark(s(s(dbl(z0))))), ACTIVE(dbl(s(z0)))) 334.34/104.39
TOP(ok(add(0, z0))) → c48(TOP(mark(z0)), ACTIVE(add(0, z0))) 334.34/104.39
TOP(ok(add(s(z0), z1))) → c48(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 334.34/104.39
TOP(ok(first(0, z0))) → c48(TOP(mark(nil)), ACTIVE(first(0, z0))) 334.34/104.39
TOP(ok(first(s(z0), cons(z1, z2)))) → c48(TOP(mark(cons(z1, first(z0, z2)))), ACTIVE(first(s(z0), cons(z1, z2)))) 334.34/104.39
TOP(ok(terms(z0))) → c48(TOP(terms(active(z0))), ACTIVE(terms(z0))) 334.34/104.39
TOP(ok(cons(z0, z1))) → c48(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 334.34/104.39
TOP(ok(recip(z0))) → c48(TOP(recip(active(z0))), ACTIVE(recip(z0))) 334.34/104.39
TOP(ok(sqr(z0))) → c48(TOP(sqr(active(z0))), ACTIVE(sqr(z0))) 334.34/104.39
TOP(ok(s(z0))) → c48(TOP(s(active(z0))), ACTIVE(s(z0))) 334.34/104.39
TOP(ok(add(z0, z1))) → c48(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 334.34/104.39
TOP(ok(add(z0, z1))) → c48(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1))) 334.34/104.39
TOP(ok(dbl(z0))) → c48(TOP(dbl(active(z0))), ACTIVE(dbl(z0))) 334.34/104.39
TOP(ok(first(z0, z1))) → c48(TOP(first(active(z0), z1)), ACTIVE(first(z0, z1))) 334.34/104.39
TOP(ok(first(z0, z1))) → c48(TOP(first(z0, active(z1))), ACTIVE(first(z0, z1)))

334.34/104.39

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.39
active(sqr(0)) → mark(0) 334.34/104.39
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.39
active(dbl(0)) → mark(0) 334.34/104.39
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.39
active(add(0, z0)) → mark(z0) 334.34/104.39
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.39
active(first(0, z0)) → mark(nil) 334.34/104.39
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.39
active(terms(z0)) → terms(active(z0)) 334.34/104.39
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.39
active(recip(z0)) → recip(active(z0)) 334.34/104.39
active(sqr(z0)) → sqr(active(z0)) 334.34/104.39
active(s(z0)) → s(active(z0)) 334.34/104.39
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.39
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.39
active(dbl(z0)) → dbl(active(z0)) 334.34/104.39
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.39
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.39
terms(mark(z0)) → mark(terms(z0)) 334.34/104.39
terms(ok(z0)) → ok(terms(z0)) 334.34/104.39
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.39
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.39
recip(mark(z0)) → mark(recip(z0)) 334.34/104.39
recip(ok(z0)) → ok(recip(z0)) 334.34/104.39
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.39
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.39
s(mark(z0)) → mark(s(z0)) 334.34/104.39
s(ok(z0)) → ok(s(z0)) 334.34/104.39
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.39
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.39
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.39
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.39
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.39
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.39
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.39
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.39
proper(terms(z0)) → terms(proper(z0)) 334.34/104.39
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.39
proper(recip(z0)) → recip(proper(z0)) 334.34/104.39
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.39
proper(s(z0)) → s(proper(z0)) 334.34/104.39
proper(0) → ok(0) 334.34/104.39
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.39
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.39
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.39
proper(nil) → ok(nil) 334.34/104.39
top(mark(z0)) → top(proper(z0)) 334.34/104.39
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.39
TOP(mark(0)) → c47(TOP(ok(0))) 334.34/104.39
TOP(mark(nil)) → c47(TOP(ok(nil)))

S tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.39
TOP(mark(0)) → c47(TOP(ok(0))) 334.34/104.39
TOP(mark(nil)) → c47(TOP(ok(nil)))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c47

334.34/104.39

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

Removed 2 trailing tuple parts

334.34/104.39

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.39
active(sqr(0)) → mark(0) 334.34/104.39
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.39
active(dbl(0)) → mark(0) 334.34/104.39
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.39
active(add(0, z0)) → mark(z0) 334.34/104.39
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.39
active(first(0, z0)) → mark(nil) 334.34/104.39
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.39
active(terms(z0)) → terms(active(z0)) 334.34/104.39
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.39
active(recip(z0)) → recip(active(z0)) 334.34/104.39
active(sqr(z0)) → sqr(active(z0)) 334.34/104.39
active(s(z0)) → s(active(z0)) 334.34/104.39
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.39
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.39
active(dbl(z0)) → dbl(active(z0)) 334.34/104.39
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.39
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.39
terms(mark(z0)) → mark(terms(z0)) 334.34/104.39
terms(ok(z0)) → ok(terms(z0)) 334.34/104.39
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.39
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.39
recip(mark(z0)) → mark(recip(z0)) 334.34/104.39
recip(ok(z0)) → ok(recip(z0)) 334.34/104.39
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.39
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.39
s(mark(z0)) → mark(s(z0)) 334.34/104.39
s(ok(z0)) → ok(s(z0)) 334.34/104.39
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.39
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.39
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.39
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.39
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.39
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.39
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.39
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.39
proper(terms(z0)) → terms(proper(z0)) 334.34/104.39
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.39
proper(recip(z0)) → recip(proper(z0)) 334.34/104.39
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.39
proper(s(z0)) → s(proper(z0)) 334.34/104.39
proper(0) → ok(0) 334.34/104.39
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.39
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.39
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.39
proper(nil) → ok(nil) 334.34/104.39
top(mark(z0)) → top(proper(z0)) 334.34/104.39
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.39
TOP(mark(0)) → c47 334.34/104.39
TOP(mark(nil)) → c47

S tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.39
TOP(mark(0)) → c47 334.34/104.39
TOP(mark(nil)) → c47

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c47

334.34/104.39

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

Removed 2 trailing nodes:

TOP(mark(nil)) → c47 334.34/104.39
TOP(mark(0)) → c47

334.34/104.39

(68) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.39
active(sqr(0)) → mark(0) 334.34/104.39
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.39
active(dbl(0)) → mark(0) 334.34/104.39
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.39
active(add(0, z0)) → mark(z0) 334.34/104.39
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.39
active(first(0, z0)) → mark(nil) 334.34/104.39
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.39
active(terms(z0)) → terms(active(z0)) 334.34/104.39
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.39
active(recip(z0)) → recip(active(z0)) 334.34/104.39
active(sqr(z0)) → sqr(active(z0)) 334.34/104.39
active(s(z0)) → s(active(z0)) 334.34/104.39
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.39
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.39
active(dbl(z0)) → dbl(active(z0)) 334.34/104.39
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.39
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.39
terms(mark(z0)) → mark(terms(z0)) 334.34/104.39
terms(ok(z0)) → ok(terms(z0)) 334.34/104.39
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.39
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.39
recip(mark(z0)) → mark(recip(z0)) 334.34/104.39
recip(ok(z0)) → ok(recip(z0)) 334.34/104.39
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.39
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.39
s(mark(z0)) → mark(s(z0)) 334.34/104.39
s(ok(z0)) → ok(s(z0)) 334.34/104.39
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.39
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.39
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.39
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.39
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.39
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.39
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.39
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.39
proper(terms(z0)) → terms(proper(z0)) 334.34/104.39
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.39
proper(recip(z0)) → recip(proper(z0)) 334.34/104.39
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.39
proper(s(z0)) → s(proper(z0)) 334.34/104.39
proper(0) → ok(0) 334.34/104.39
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.39
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.39
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.39
proper(nil) → ok(nil) 334.34/104.39
top(mark(z0)) → top(proper(z0)) 334.34/104.39
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.39

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

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

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0))

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

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 334.34/104.39

POL(ADD(x₁, x₂)) = 0 334.34/104.39
POL(CONS(x₁, x₂)) = 0 334.34/104.39
POL(DBL(x₁)) = 0 334.34/104.39
POL(FIRST(x₁, x₂)) = 0 334.34/104.39
POL(RECIP(x₁)) = 0 334.34/104.39
POL(S(x₁)) = 0 334.34/104.39
POL(SQR(x₁)) = x₁ 334.34/104.39
POL(TERMS(x₁)) = 0 334.34/104.39
POL(c19(x₁)) = x₁ 334.34/104.39
POL(c20(x₁)) = x₁ 334.34/104.39
POL(c21(x₁)) = x₁ 334.34/104.39
POL(c22(x₁)) = x₁ 334.34/104.39
POL(c23(x₁)) = x₁ 334.34/104.39
POL(c24(x₁)) = x₁ 334.34/104.39
POL(c25(x₁)) = x₁ 334.34/104.39
POL(c26(x₁)) = x₁ 334.34/104.39
POL(c27(x₁)) = x₁ 334.34/104.39
POL(c28(x₁)) = x₁ 334.34/104.39
POL(c29(x₁)) = x₁ 334.34/104.39
POL(c30(x₁)) = x₁ 334.34/104.39
POL(c31(x₁)) = x₁ 334.34/104.39
POL(c32(x₁)) = x₁ 334.34/104.39
POL(c33(x₁)) = x₁ 334.34/104.39
POL(c34(x₁)) = x₁ 334.34/104.39
POL(c35(x₁)) = x₁ 334.34/104.39
POL(c36(x₁)) = x₁ 334.34/104.39
POL(mark(x₁)) = [1] + x₁ 334.34/104.39
POL(ok(x₁)) = [1] + x₁

334.34/104.39

(70) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.39
active(sqr(0)) → mark(0) 334.34/104.39
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.39
active(dbl(0)) → mark(0) 334.34/104.39
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.39
active(add(0, z0)) → mark(z0) 334.34/104.39
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.39
active(first(0, z0)) → mark(nil) 334.34/104.39
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.39
active(terms(z0)) → terms(active(z0)) 334.34/104.39
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.39
active(recip(z0)) → recip(active(z0)) 334.34/104.39
active(sqr(z0)) → sqr(active(z0)) 334.34/104.39
active(s(z0)) → s(active(z0)) 334.34/104.39
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.39
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.39
active(dbl(z0)) → dbl(active(z0)) 334.34/104.39
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.39
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.39
terms(mark(z0)) → mark(terms(z0)) 334.34/104.39
terms(ok(z0)) → ok(terms(z0)) 334.34/104.39
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.39
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.39
recip(mark(z0)) → mark(recip(z0)) 334.34/104.39
recip(ok(z0)) → ok(recip(z0)) 334.34/104.39
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.39
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.39
s(mark(z0)) → mark(s(z0)) 334.34/104.39
s(ok(z0)) → ok(s(z0)) 334.34/104.39
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.39
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.39
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.39
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.39
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.39
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.39
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.39
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.39
proper(terms(z0)) → terms(proper(z0)) 334.34/104.39
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.39
proper(recip(z0)) → recip(proper(z0)) 334.34/104.39
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.39
proper(s(z0)) → s(proper(z0)) 334.34/104.39
proper(0) → ok(0) 334.34/104.39
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.39
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.39
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.39
proper(nil) → ok(nil) 334.34/104.39
top(mark(z0)) → top(proper(z0)) 334.34/104.39
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

K tuples:

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0))

Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.39

(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.

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0))

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

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.39
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.39
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.39
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.39
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.39
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.39
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.39
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.39
S(mark(z0)) → c27(S(z0)) 334.34/104.39
S(ok(z0)) → c28(S(z0)) 334.34/104.39
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.39
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.39
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.39
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.39
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.39
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.39
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.39
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 334.34/104.39

POL(ADD(x₁, x₂)) = 0 334.34/104.39
POL(CONS(x₁, x₂)) = 0 334.34/104.39
POL(DBL(x₁)) = 0 334.34/104.39
POL(FIRST(x₁, x₂)) = 0 334.34/104.39
POL(RECIP(x₁)) = 0 334.34/104.39
POL(S(x₁)) = 0 334.34/104.39
POL(SQR(x₁)) = [3]x₁ 334.34/104.39
POL(TERMS(x₁)) = [2]x₁ 334.34/104.39
POL(c19(x₁)) = x₁ 334.34/104.39
POL(c20(x₁)) = x₁ 334.34/104.40
POL(c21(x₁)) = x₁ 334.34/104.40
POL(c22(x₁)) = x₁ 334.34/104.40
POL(c23(x₁)) = x₁ 334.34/104.40
POL(c24(x₁)) = x₁ 334.34/104.40
POL(c25(x₁)) = x₁ 334.34/104.40
POL(c26(x₁)) = x₁ 334.34/104.40
POL(c27(x₁)) = x₁ 334.34/104.40
POL(c28(x₁)) = x₁ 334.34/104.40
POL(c29(x₁)) = x₁ 334.34/104.40
POL(c30(x₁)) = x₁ 334.34/104.40
POL(c31(x₁)) = x₁ 334.34/104.40
POL(c32(x₁)) = x₁ 334.34/104.40
POL(c33(x₁)) = x₁ 334.34/104.40
POL(c34(x₁)) = x₁ 334.34/104.40
POL(c35(x₁)) = x₁ 334.34/104.40
POL(c36(x₁)) = x₁ 334.34/104.40
POL(mark(x₁)) = [1] + x₁ 334.34/104.40
POL(ok(x₁)) = [1] + x₁

334.34/104.40

(72) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.40
active(sqr(0)) → mark(0) 334.34/104.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.40
active(dbl(0)) → mark(0) 334.34/104.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.40
active(add(0, z0)) → mark(z0) 334.34/104.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.40
active(first(0, z0)) → mark(nil) 334.34/104.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.40
active(terms(z0)) → terms(active(z0)) 334.34/104.40
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.40
active(recip(z0)) → recip(active(z0)) 334.34/104.40
active(sqr(z0)) → sqr(active(z0)) 334.34/104.40
active(s(z0)) → s(active(z0)) 334.34/104.40
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.40
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.40
active(dbl(z0)) → dbl(active(z0)) 334.34/104.40
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.40
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.40
terms(mark(z0)) → mark(terms(z0)) 334.34/104.40
terms(ok(z0)) → ok(terms(z0)) 334.34/104.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.40
recip(mark(z0)) → mark(recip(z0)) 334.34/104.40
recip(ok(z0)) → ok(recip(z0)) 334.34/104.40
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.40
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.40
s(mark(z0)) → mark(s(z0)) 334.34/104.40
s(ok(z0)) → ok(s(z0)) 334.34/104.40
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.40
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.40
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.40
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.40
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.40
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.40
proper(terms(z0)) → terms(proper(z0)) 334.34/104.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.40
proper(recip(z0)) → recip(proper(z0)) 334.34/104.40
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.40
proper(s(z0)) → s(proper(z0)) 334.34/104.40
proper(0) → ok(0) 334.34/104.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.40
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.40
proper(nil) → ok(nil) 334.34/104.40
top(mark(z0)) → top(proper(z0)) 334.34/104.40
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:

CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

K tuples:

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0))

Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.40

(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.

RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0))

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

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 334.34/104.40

POL(ADD(x₁, x₂)) = 0 334.34/104.40
POL(CONS(x₁, x₂)) = 0 334.34/104.40
POL(DBL(x₁)) = 0 334.34/104.40
POL(FIRST(x₁, x₂)) = 0 334.34/104.40
POL(RECIP(x₁)) = x₁ 334.34/104.40
POL(S(x₁)) = 0 334.34/104.40
POL(SQR(x₁)) = [5]x₁ 334.34/104.40
POL(TERMS(x₁)) = [3]x₁ 334.34/104.40
POL(c19(x₁)) = x₁ 334.34/104.40
POL(c20(x₁)) = x₁ 334.34/104.40
POL(c21(x₁)) = x₁ 334.34/104.40
POL(c22(x₁)) = x₁ 334.34/104.40
POL(c23(x₁)) = x₁ 334.34/104.40
POL(c24(x₁)) = x₁ 334.34/104.40
POL(c25(x₁)) = x₁ 334.34/104.40
POL(c26(x₁)) = x₁ 334.34/104.40
POL(c27(x₁)) = x₁ 334.34/104.40
POL(c28(x₁)) = x₁ 334.34/104.40
POL(c29(x₁)) = x₁ 334.34/104.40
POL(c30(x₁)) = x₁ 334.34/104.40
POL(c31(x₁)) = x₁ 334.34/104.40
POL(c32(x₁)) = x₁ 334.34/104.40
POL(c33(x₁)) = x₁ 334.34/104.40
POL(c34(x₁)) = x₁ 334.34/104.40
POL(c35(x₁)) = x₁ 334.34/104.40
POL(c36(x₁)) = x₁ 334.34/104.40
POL(mark(x₁)) = [1] + x₁ 334.34/104.40
POL(ok(x₁)) = [1] + x₁

334.34/104.40

(74) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.40
active(sqr(0)) → mark(0) 334.34/104.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.40
active(dbl(0)) → mark(0) 334.34/104.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.40
active(add(0, z0)) → mark(z0) 334.34/104.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.40
active(first(0, z0)) → mark(nil) 334.34/104.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.40
active(terms(z0)) → terms(active(z0)) 334.34/104.40
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.40
active(recip(z0)) → recip(active(z0)) 334.34/104.40
active(sqr(z0)) → sqr(active(z0)) 334.34/104.40
active(s(z0)) → s(active(z0)) 334.34/104.40
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.40
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.40
active(dbl(z0)) → dbl(active(z0)) 334.34/104.40
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.40
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.40
terms(mark(z0)) → mark(terms(z0)) 334.34/104.40
terms(ok(z0)) → ok(terms(z0)) 334.34/104.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.40
recip(mark(z0)) → mark(recip(z0)) 334.34/104.40
recip(ok(z0)) → ok(recip(z0)) 334.34/104.40
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.40
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.40
s(mark(z0)) → mark(s(z0)) 334.34/104.40
s(ok(z0)) → ok(s(z0)) 334.34/104.40
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.40
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.40
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.40
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.40
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.40
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.40
proper(terms(z0)) → terms(proper(z0)) 334.34/104.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.40
proper(recip(z0)) → recip(proper(z0)) 334.34/104.40
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.40
proper(s(z0)) → s(proper(z0)) 334.34/104.40
proper(0) → ok(0) 334.34/104.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.40
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.40
proper(nil) → ok(nil) 334.34/104.40
top(mark(z0)) → top(proper(z0)) 334.34/104.40
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:

CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

K tuples:

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0))

Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.40

(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.

DBL(ok(z0)) → c33(DBL(z0))

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

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 334.34/104.40

POL(ADD(x₁, x₂)) = 0 334.34/104.40
POL(CONS(x₁, x₂)) = 0 334.34/104.40
POL(DBL(x₁)) = x₁ 334.34/104.40
POL(FIRST(x₁, x₂)) = 0 334.34/104.40
POL(RECIP(x₁)) = [5]x₁ 334.34/104.40
POL(S(x₁)) = 0 334.34/104.40
POL(SQR(x₁)) = [3]x₁ 334.34/104.40
POL(TERMS(x₁)) = [3]x₁ 334.34/104.40
POL(c19(x₁)) = x₁ 334.34/104.40
POL(c20(x₁)) = x₁ 334.34/104.40
POL(c21(x₁)) = x₁ 334.34/104.40
POL(c22(x₁)) = x₁ 334.34/104.40
POL(c23(x₁)) = x₁ 334.34/104.40
POL(c24(x₁)) = x₁ 334.34/104.40
POL(c25(x₁)) = x₁ 334.34/104.40
POL(c26(x₁)) = x₁ 334.34/104.40
POL(c27(x₁)) = x₁ 334.34/104.40
POL(c28(x₁)) = x₁ 334.34/104.40
POL(c29(x₁)) = x₁ 334.34/104.40
POL(c30(x₁)) = x₁ 334.34/104.40
POL(c31(x₁)) = x₁ 334.34/104.40
POL(c32(x₁)) = x₁ 334.34/104.40
POL(c33(x₁)) = x₁ 334.34/104.40
POL(c34(x₁)) = x₁ 334.34/104.40
POL(c35(x₁)) = x₁ 334.34/104.40
POL(c36(x₁)) = x₁ 334.34/104.40
POL(mark(x₁)) = x₁ 334.34/104.40
POL(ok(x₁)) = [1] + x₁

334.34/104.40

(76) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.40
active(sqr(0)) → mark(0) 334.34/104.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.40
active(dbl(0)) → mark(0) 334.34/104.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.40
active(add(0, z0)) → mark(z0) 334.34/104.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.40
active(first(0, z0)) → mark(nil) 334.34/104.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.40
active(terms(z0)) → terms(active(z0)) 334.34/104.40
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.40
active(recip(z0)) → recip(active(z0)) 334.34/104.40
active(sqr(z0)) → sqr(active(z0)) 334.34/104.40
active(s(z0)) → s(active(z0)) 334.34/104.40
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.40
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.40
active(dbl(z0)) → dbl(active(z0)) 334.34/104.40
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.40
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.40
terms(mark(z0)) → mark(terms(z0)) 334.34/104.40
terms(ok(z0)) → ok(terms(z0)) 334.34/104.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.40
recip(mark(z0)) → mark(recip(z0)) 334.34/104.40
recip(ok(z0)) → ok(recip(z0)) 334.34/104.40
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.40
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.40
s(mark(z0)) → mark(s(z0)) 334.34/104.40
s(ok(z0)) → ok(s(z0)) 334.34/104.40
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.40
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.40
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.40
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.40
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.40
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.40
proper(terms(z0)) → terms(proper(z0)) 334.34/104.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.40
proper(recip(z0)) → recip(proper(z0)) 334.34/104.40
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.40
proper(s(z0)) → s(proper(z0)) 334.34/104.40
proper(0) → ok(0) 334.34/104.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.40
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.40
proper(nil) → ok(nil) 334.34/104.40
top(mark(z0)) → top(proper(z0)) 334.34/104.40
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:

CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

K tuples:

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0))

Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.40

(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.

ADD(mark(z0), z1) → c29(ADD(z0, z1))

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

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 334.34/104.40

POL(ADD(x₁, x₂)) = x₁ 334.34/104.40
POL(CONS(x₁, x₂)) = 0 334.34/104.40
POL(DBL(x₁)) = 0 334.34/104.40
POL(FIRST(x₁, x₂)) = 0 334.34/104.40
POL(RECIP(x₁)) = [5]x₁ 334.34/104.40
POL(S(x₁)) = 0 334.34/104.40
POL(SQR(x₁)) = [3]x₁ 334.34/104.40
POL(TERMS(x₁)) = [3]x₁ 334.34/104.40
POL(c19(x₁)) = x₁ 334.34/104.40
POL(c20(x₁)) = x₁ 334.34/104.40
POL(c21(x₁)) = x₁ 334.34/104.40
POL(c22(x₁)) = x₁ 334.34/104.40
POL(c23(x₁)) = x₁ 334.34/104.40
POL(c24(x₁)) = x₁ 334.34/104.40
POL(c25(x₁)) = x₁ 334.34/104.40
POL(c26(x₁)) = x₁ 334.34/104.40
POL(c27(x₁)) = x₁ 334.34/104.40
POL(c28(x₁)) = x₁ 334.34/104.40
POL(c29(x₁)) = x₁ 334.34/104.40
POL(c30(x₁)) = x₁ 334.34/104.40
POL(c31(x₁)) = x₁ 334.34/104.40
POL(c32(x₁)) = x₁ 334.34/104.40
POL(c33(x₁)) = x₁ 334.34/104.40
POL(c34(x₁)) = x₁ 334.34/104.40
POL(c35(x₁)) = x₁ 334.34/104.40
POL(c36(x₁)) = x₁ 334.34/104.40
POL(mark(x₁)) = [1] + x₁ 334.34/104.40
POL(ok(x₁)) = x₁

334.34/104.40

(78) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.40
active(sqr(0)) → mark(0) 334.34/104.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.40
active(dbl(0)) → mark(0) 334.34/104.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.40
active(add(0, z0)) → mark(z0) 334.34/104.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.40
active(first(0, z0)) → mark(nil) 334.34/104.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.40
active(terms(z0)) → terms(active(z0)) 334.34/104.40
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.40
active(recip(z0)) → recip(active(z0)) 334.34/104.40
active(sqr(z0)) → sqr(active(z0)) 334.34/104.40
active(s(z0)) → s(active(z0)) 334.34/104.40
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.40
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.40
active(dbl(z0)) → dbl(active(z0)) 334.34/104.40
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.40
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.40
terms(mark(z0)) → mark(terms(z0)) 334.34/104.40
terms(ok(z0)) → ok(terms(z0)) 334.34/104.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.40
recip(mark(z0)) → mark(recip(z0)) 334.34/104.40
recip(ok(z0)) → ok(recip(z0)) 334.34/104.40
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.40
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.40
s(mark(z0)) → mark(s(z0)) 334.34/104.40
s(ok(z0)) → ok(s(z0)) 334.34/104.40
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.40
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.40
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.40
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.40
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.40
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.40
proper(terms(z0)) → terms(proper(z0)) 334.34/104.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.40
proper(recip(z0)) → recip(proper(z0)) 334.34/104.40
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.40
proper(s(z0)) → s(proper(z0)) 334.34/104.40
proper(0) → ok(0) 334.34/104.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.40
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.40
proper(nil) → ok(nil) 334.34/104.40
top(mark(z0)) → top(proper(z0)) 334.34/104.40
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:

CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

K tuples:

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1))

Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.40

(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.

DBL(mark(z0)) → c32(DBL(z0))

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

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 334.34/104.40

POL(ADD(x₁, x₂)) = 0 334.34/104.40
POL(CONS(x₁, x₂)) = 0 334.34/104.40
POL(DBL(x₁)) = x₁ 334.34/104.40
POL(FIRST(x₁, x₂)) = 0 334.34/104.40
POL(RECIP(x₁)) = [5]x₁ 334.34/104.40
POL(S(x₁)) = 0 334.34/104.40
POL(SQR(x₁)) = [3]x₁ 334.34/104.40
POL(TERMS(x₁)) = [3]x₁ 334.34/104.40
POL(c19(x₁)) = x₁ 334.34/104.40
POL(c20(x₁)) = x₁ 334.34/104.40
POL(c21(x₁)) = x₁ 334.34/104.40
POL(c22(x₁)) = x₁ 334.34/104.40
POL(c23(x₁)) = x₁ 334.34/104.40
POL(c24(x₁)) = x₁ 334.34/104.40
POL(c25(x₁)) = x₁ 334.34/104.40
POL(c26(x₁)) = x₁ 334.34/104.40
POL(c27(x₁)) = x₁ 334.34/104.40
POL(c28(x₁)) = x₁ 334.34/104.40
POL(c29(x₁)) = x₁ 334.34/104.40
POL(c30(x₁)) = x₁ 334.34/104.40
POL(c31(x₁)) = x₁ 334.34/104.40
POL(c32(x₁)) = x₁ 334.34/104.40
POL(c33(x₁)) = x₁ 334.34/104.40
POL(c34(x₁)) = x₁ 334.34/104.40
POL(c35(x₁)) = x₁ 334.34/104.40
POL(c36(x₁)) = x₁ 334.34/104.40
POL(mark(x₁)) = [1] + x₁ 334.34/104.40
POL(ok(x₁)) = x₁

334.34/104.40

(80) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.40
active(sqr(0)) → mark(0) 334.34/104.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.40
active(dbl(0)) → mark(0) 334.34/104.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.40
active(add(0, z0)) → mark(z0) 334.34/104.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.40
active(first(0, z0)) → mark(nil) 334.34/104.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.40
active(terms(z0)) → terms(active(z0)) 334.34/104.40
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.40
active(recip(z0)) → recip(active(z0)) 334.34/104.40
active(sqr(z0)) → sqr(active(z0)) 334.34/104.40
active(s(z0)) → s(active(z0)) 334.34/104.40
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.40
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.40
active(dbl(z0)) → dbl(active(z0)) 334.34/104.40
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.40
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.40
terms(mark(z0)) → mark(terms(z0)) 334.34/104.40
terms(ok(z0)) → ok(terms(z0)) 334.34/104.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.40
recip(mark(z0)) → mark(recip(z0)) 334.34/104.40
recip(ok(z0)) → ok(recip(z0)) 334.34/104.40
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.40
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.40
s(mark(z0)) → mark(s(z0)) 334.34/104.40
s(ok(z0)) → ok(s(z0)) 334.34/104.40
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.40
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.40
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.40
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.40
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.40
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.40
proper(terms(z0)) → terms(proper(z0)) 334.34/104.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.40
proper(recip(z0)) → recip(proper(z0)) 334.34/104.40
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.40
proper(s(z0)) → s(proper(z0)) 334.34/104.40
proper(0) → ok(0) 334.34/104.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.40
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.40
proper(nil) → ok(nil) 334.34/104.40
top(mark(z0)) → top(proper(z0)) 334.34/104.40
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:

CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

K tuples:

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0))

Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.40

(81) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))) transformation)

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

CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1))

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

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 334.34/104.40

POL(ADD(x₁, x₂)) = 0 334.34/104.40
POL(CONS(x₁, x₂)) = [2]x₂² 334.34/104.40
POL(DBL(x₁)) = 0 334.34/104.40
POL(FIRST(x₁, x₂)) = 0 334.34/104.40
POL(RECIP(x₁)) = 0 334.34/104.40
POL(S(x₁)) = 0 334.34/104.40
POL(SQR(x₁)) = 0 334.34/104.40
POL(TERMS(x₁)) = 0 334.34/104.40
POL(c19(x₁)) = x₁ 334.34/104.40
POL(c20(x₁)) = x₁ 334.34/104.40
POL(c21(x₁)) = x₁ 334.34/104.40
POL(c22(x₁)) = x₁ 334.34/104.40
POL(c23(x₁)) = x₁ 334.34/104.40
POL(c24(x₁)) = x₁ 334.34/104.40
POL(c25(x₁)) = x₁ 334.34/104.40
POL(c26(x₁)) = x₁ 334.34/104.40
POL(c27(x₁)) = x₁ 334.34/104.40
POL(c28(x₁)) = x₁ 334.34/104.40
POL(c29(x₁)) = x₁ 334.34/104.40
POL(c30(x₁)) = x₁ 334.34/104.40
POL(c31(x₁)) = x₁ 334.34/104.40
POL(c32(x₁)) = x₁ 334.34/104.40
POL(c33(x₁)) = x₁ 334.34/104.40
POL(c34(x₁)) = x₁ 334.34/104.40
POL(c35(x₁)) = x₁ 334.34/104.40
POL(c36(x₁)) = x₁ 334.34/104.40
POL(mark(x₁)) = 0 334.34/104.40
POL(ok(x₁)) = [1] + x₁

334.34/104.40

(82) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.40
active(sqr(0)) → mark(0) 334.34/104.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.40
active(dbl(0)) → mark(0) 334.34/104.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.40
active(add(0, z0)) → mark(z0) 334.34/104.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.40
active(first(0, z0)) → mark(nil) 334.34/104.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.40
active(terms(z0)) → terms(active(z0)) 334.34/104.40
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.40
active(recip(z0)) → recip(active(z0)) 334.34/104.40
active(sqr(z0)) → sqr(active(z0)) 334.34/104.40
active(s(z0)) → s(active(z0)) 334.34/104.40
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.40
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.40
active(dbl(z0)) → dbl(active(z0)) 334.34/104.40
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.40
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.40
terms(mark(z0)) → mark(terms(z0)) 334.34/104.40
terms(ok(z0)) → ok(terms(z0)) 334.34/104.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.40
recip(mark(z0)) → mark(recip(z0)) 334.34/104.40
recip(ok(z0)) → ok(recip(z0)) 334.34/104.40
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.40
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.40
s(mark(z0)) → mark(s(z0)) 334.34/104.40
s(ok(z0)) → ok(s(z0)) 334.34/104.40
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.40
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.40
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.40
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.40
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.40
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.40
proper(terms(z0)) → terms(proper(z0)) 334.34/104.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.40
proper(recip(z0)) → recip(proper(z0)) 334.34/104.40
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.40
proper(s(z0)) → s(proper(z0)) 334.34/104.40
proper(0) → ok(0) 334.34/104.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.40
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.40
proper(nil) → ok(nil) 334.34/104.40
top(mark(z0)) → top(proper(z0)) 334.34/104.40
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:

CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

K tuples:

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1))

Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.40

(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.

CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

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

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 334.34/104.40

POL(ADD(x₁, x₂)) = 0 334.34/104.40
POL(CONS(x₁, x₂)) = [2]x₁ + [3]x₂ 334.34/104.40
POL(DBL(x₁)) = [3]x₁ 334.34/104.40
POL(FIRST(x₁, x₂)) = [2]x₂ 334.34/104.40
POL(RECIP(x₁)) = [5]x₁ 334.34/104.40
POL(S(x₁)) = x₁ 334.34/104.40
POL(SQR(x₁)) = [3]x₁ 334.34/104.40
POL(TERMS(x₁)) = [5]x₁ 334.34/104.40
POL(c19(x₁)) = x₁ 334.34/104.40
POL(c20(x₁)) = x₁ 334.34/104.40
POL(c21(x₁)) = x₁ 334.34/104.40
POL(c22(x₁)) = x₁ 334.34/104.40
POL(c23(x₁)) = x₁ 334.34/104.40
POL(c24(x₁)) = x₁ 334.34/104.40
POL(c25(x₁)) = x₁ 334.34/104.40
POL(c26(x₁)) = x₁ 334.34/104.40
POL(c27(x₁)) = x₁ 334.34/104.40
POL(c28(x₁)) = x₁ 334.34/104.40
POL(c29(x₁)) = x₁ 334.34/104.40
POL(c30(x₁)) = x₁ 334.34/104.40
POL(c31(x₁)) = x₁ 334.34/104.40
POL(c32(x₁)) = x₁ 334.34/104.40
POL(c33(x₁)) = x₁ 334.34/104.40
POL(c34(x₁)) = x₁ 334.34/104.40
POL(c35(x₁)) = x₁ 334.34/104.40
POL(c36(x₁)) = x₁ 334.34/104.40
POL(mark(x₁)) = [2] + x₁ 334.34/104.40
POL(ok(x₁)) = [1] + x₁

334.34/104.40

(84) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.40
active(sqr(0)) → mark(0) 334.34/104.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.40
active(dbl(0)) → mark(0) 334.34/104.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.40
active(add(0, z0)) → mark(z0) 334.34/104.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.40
active(first(0, z0)) → mark(nil) 334.34/104.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.40
active(terms(z0)) → terms(active(z0)) 334.34/104.40
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.40
active(recip(z0)) → recip(active(z0)) 334.34/104.40
active(sqr(z0)) → sqr(active(z0)) 334.34/104.40
active(s(z0)) → s(active(z0)) 334.34/104.40
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.40
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.40
active(dbl(z0)) → dbl(active(z0)) 334.34/104.40
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.40
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.40
terms(mark(z0)) → mark(terms(z0)) 334.34/104.40
terms(ok(z0)) → ok(terms(z0)) 334.34/104.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.40
recip(mark(z0)) → mark(recip(z0)) 334.34/104.40
recip(ok(z0)) → ok(recip(z0)) 334.34/104.40
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.40
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.40
s(mark(z0)) → mark(s(z0)) 334.34/104.40
s(ok(z0)) → ok(s(z0)) 334.34/104.40
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.40
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.40
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.40
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.40
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.40
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.40
proper(terms(z0)) → terms(proper(z0)) 334.34/104.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.40
proper(recip(z0)) → recip(proper(z0)) 334.34/104.40
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.40
proper(s(z0)) → s(proper(z0)) 334.34/104.40
proper(0) → ok(0) 334.34/104.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.40
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.40
proper(nil) → ok(nil) 334.34/104.40
top(mark(z0)) → top(proper(z0)) 334.34/104.40
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:

ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1))

K tuples:

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.40

(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)) → c30(ADD(z0, z1))

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

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 334.34/104.40

POL(ADD(x₁, x₂)) = x₂ 334.34/104.40
POL(CONS(x₁, x₂)) = [5]x₁ + [5]x₂ 334.34/104.40
POL(DBL(x₁)) = [3]x₁ 334.34/104.40
POL(FIRST(x₁, x₂)) = [5]x₂ 334.34/104.40
POL(RECIP(x₁)) = [3]x₁ 334.34/104.40
POL(S(x₁)) = [5]x₁ 334.34/104.40
POL(SQR(x₁)) = [3]x₁ 334.34/104.40
POL(TERMS(x₁)) = [3]x₁ 334.34/104.40
POL(c19(x₁)) = x₁ 334.34/104.40
POL(c20(x₁)) = x₁ 334.34/104.40
POL(c21(x₁)) = x₁ 334.34/104.40
POL(c22(x₁)) = x₁ 334.34/104.40
POL(c23(x₁)) = x₁ 334.34/104.40
POL(c24(x₁)) = x₁ 334.34/104.40
POL(c25(x₁)) = x₁ 334.34/104.40
POL(c26(x₁)) = x₁ 334.34/104.40
POL(c27(x₁)) = x₁ 334.34/104.40
POL(c28(x₁)) = x₁ 334.34/104.40
POL(c29(x₁)) = x₁ 334.34/104.40
POL(c30(x₁)) = x₁ 334.34/104.40
POL(c31(x₁)) = x₁ 334.34/104.40
POL(c32(x₁)) = x₁ 334.34/104.40
POL(c33(x₁)) = x₁ 334.34/104.40
POL(c34(x₁)) = x₁ 334.34/104.40
POL(c35(x₁)) = x₁ 334.34/104.40
POL(c36(x₁)) = x₁ 334.34/104.40
POL(mark(x₁)) = [1] + x₁ 334.34/104.40
POL(ok(x₁)) = x₁

334.34/104.40

(86) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.40
active(sqr(0)) → mark(0) 334.34/104.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.40
active(dbl(0)) → mark(0) 334.34/104.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.40
active(add(0, z0)) → mark(z0) 334.34/104.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.40
active(first(0, z0)) → mark(nil) 334.34/104.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.40
active(terms(z0)) → terms(active(z0)) 334.34/104.40
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.40
active(recip(z0)) → recip(active(z0)) 334.34/104.40
active(sqr(z0)) → sqr(active(z0)) 334.34/104.40
active(s(z0)) → s(active(z0)) 334.34/104.40
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.40
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.40
active(dbl(z0)) → dbl(active(z0)) 334.34/104.40
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.40
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.40
terms(mark(z0)) → mark(terms(z0)) 334.34/104.40
terms(ok(z0)) → ok(terms(z0)) 334.34/104.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.40
recip(mark(z0)) → mark(recip(z0)) 334.34/104.40
recip(ok(z0)) → ok(recip(z0)) 334.34/104.40
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.40
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.40
s(mark(z0)) → mark(s(z0)) 334.34/104.40
s(ok(z0)) → ok(s(z0)) 334.34/104.40
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.40
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.40
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.40
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.40
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.40
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.40
proper(terms(z0)) → terms(proper(z0)) 334.34/104.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.40
proper(recip(z0)) → recip(proper(z0)) 334.34/104.40
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.40
proper(s(z0)) → s(proper(z0)) 334.34/104.40
proper(0) → ok(0) 334.34/104.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.40
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.40
proper(nil) → ok(nil) 334.34/104.40
top(mark(z0)) → top(proper(z0)) 334.34/104.40
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:

ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1))

K tuples:

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1))

Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.40

(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.

ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1))

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

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 334.34/104.40

POL(ADD(x₁, x₂)) = x₁ 334.34/104.40
POL(CONS(x₁, x₂)) = [3]x₁ + [5]x₂ 334.34/104.40
POL(DBL(x₁)) = [5]x₁ 334.34/104.40
POL(FIRST(x₁, x₂)) = [3]x₂ 334.34/104.40
POL(RECIP(x₁)) = [5]x₁ 334.34/104.40
POL(S(x₁)) = [3]x₁ 334.34/104.40
POL(SQR(x₁)) = [3]x₁ 334.34/104.40
POL(TERMS(x₁)) = [3]x₁ 334.34/104.40
POL(c19(x₁)) = x₁ 334.34/104.40
POL(c20(x₁)) = x₁ 334.34/104.40
POL(c21(x₁)) = x₁ 334.34/104.40
POL(c22(x₁)) = x₁ 334.34/104.40
POL(c23(x₁)) = x₁ 334.34/104.40
POL(c24(x₁)) = x₁ 334.34/104.40
POL(c25(x₁)) = x₁ 334.34/104.40
POL(c26(x₁)) = x₁ 334.34/104.40
POL(c27(x₁)) = x₁ 334.34/104.40
POL(c28(x₁)) = x₁ 334.34/104.40
POL(c29(x₁)) = x₁ 334.34/104.40
POL(c30(x₁)) = x₁ 334.34/104.40
POL(c31(x₁)) = x₁ 334.34/104.40
POL(c32(x₁)) = x₁ 334.34/104.40
POL(c33(x₁)) = x₁ 334.34/104.40
POL(c34(x₁)) = x₁ 334.34/104.40
POL(c35(x₁)) = x₁ 334.34/104.40
POL(c36(x₁)) = x₁ 334.34/104.40
POL(mark(x₁)) = [1] + x₁ 334.34/104.40
POL(ok(x₁)) = [2] + x₁

334.34/104.40

(88) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.40
active(sqr(0)) → mark(0) 334.34/104.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.40
active(dbl(0)) → mark(0) 334.34/104.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.40
active(add(0, z0)) → mark(z0) 334.34/104.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.40
active(first(0, z0)) → mark(nil) 334.34/104.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.40
active(terms(z0)) → terms(active(z0)) 334.34/104.40
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.40
active(recip(z0)) → recip(active(z0)) 334.34/104.40
active(sqr(z0)) → sqr(active(z0)) 334.34/104.40
active(s(z0)) → s(active(z0)) 334.34/104.40
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.40
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.40
active(dbl(z0)) → dbl(active(z0)) 334.34/104.40
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.40
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.40
terms(mark(z0)) → mark(terms(z0)) 334.34/104.40
terms(ok(z0)) → ok(terms(z0)) 334.34/104.40
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.40
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.40
recip(mark(z0)) → mark(recip(z0)) 334.34/104.40
recip(ok(z0)) → ok(recip(z0)) 334.34/104.40
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.40
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.40
s(mark(z0)) → mark(s(z0)) 334.34/104.40
s(ok(z0)) → ok(s(z0)) 334.34/104.40
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.40
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.40
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.40
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.40
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.40
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.40
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.40
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.40
proper(terms(z0)) → terms(proper(z0)) 334.34/104.40
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.40
proper(recip(z0)) → recip(proper(z0)) 334.34/104.40
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.40
proper(s(z0)) → s(proper(z0)) 334.34/104.40
proper(0) → ok(0) 334.34/104.40
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.40
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.40
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.40
proper(nil) → ok(nil) 334.34/104.40
top(mark(z0)) → top(proper(z0)) 334.34/104.40
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:

FIRST(mark(z0), z1) → c34(FIRST(z0, z1))

K tuples:

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1))

Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.40

(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.

FIRST(mark(z0), z1) → c34(FIRST(z0, z1))

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

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.40
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.40
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.40
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.40
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.40
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.40
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.40
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.40
S(mark(z0)) → c27(S(z0)) 334.34/104.40
S(ok(z0)) → c28(S(z0)) 334.34/104.40
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.40
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.40
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.40
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.40
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.40
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.40
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.40
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 334.34/104.40

POL(ADD(x₁, x₂)) = [3]x₁ + [3]x₂ 334.34/104.40
POL(CONS(x₁, x₂)) = [5]x₁ + [3]x₂ 334.34/104.40
POL(DBL(x₁)) = [5]x₁ 334.34/104.40
POL(FIRST(x₁, x₂)) = [5]x₁ + [3]x₂ 334.34/104.40
POL(RECIP(x₁)) = [5]x₁ 334.34/104.40
POL(S(x₁)) = [5]x₁ 334.34/104.40
POL(SQR(x₁)) = [5]x₁ 334.34/104.40
POL(TERMS(x₁)) = [3]x₁ 334.34/104.40
POL(c19(x₁)) = x₁ 334.34/104.40
POL(c20(x₁)) = x₁ 334.34/104.40
POL(c21(x₁)) = x₁ 334.34/104.40
POL(c22(x₁)) = x₁ 334.34/104.40
POL(c23(x₁)) = x₁ 334.34/104.40
POL(c24(x₁)) = x₁ 334.34/104.40
POL(c25(x₁)) = x₁ 334.34/104.40
POL(c26(x₁)) = x₁ 334.34/104.40
POL(c27(x₁)) = x₁ 334.34/104.40
POL(c28(x₁)) = x₁ 334.34/104.40
POL(c29(x₁)) = x₁ 334.34/104.40
POL(c30(x₁)) = x₁ 334.34/104.40
POL(c31(x₁)) = x₁ 334.34/104.40
POL(c32(x₁)) = x₁ 334.34/104.40
POL(c33(x₁)) = x₁ 334.34/104.40
POL(c34(x₁)) = x₁ 334.34/104.40
POL(c35(x₁)) = x₁ 334.34/104.40
POL(c36(x₁)) = x₁ 334.34/104.40
POL(mark(x₁)) = [1] + x₁ 334.34/104.40
POL(ok(x₁)) = x₁

334.34/104.40

(90) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(terms(z0)) → mark(cons(recip(sqr(z0)), terms(s(z0)))) 334.34/104.40
active(sqr(0)) → mark(0) 334.34/104.40
active(sqr(s(z0))) → mark(s(add(sqr(z0), dbl(z0)))) 334.34/104.40
active(dbl(0)) → mark(0) 334.34/104.40
active(dbl(s(z0))) → mark(s(s(dbl(z0)))) 334.34/104.40
active(add(0, z0)) → mark(z0) 334.34/104.40
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 334.34/104.40
active(first(0, z0)) → mark(nil) 334.34/104.40
active(first(s(z0), cons(z1, z2))) → mark(cons(z1, first(z0, z2))) 334.34/104.40
active(terms(z0)) → terms(active(z0)) 334.34/104.40
active(cons(z0, z1)) → cons(active(z0), z1) 334.34/104.40
active(recip(z0)) → recip(active(z0)) 334.34/104.40
active(sqr(z0)) → sqr(active(z0)) 334.34/104.41
active(s(z0)) → s(active(z0)) 334.34/104.41
active(add(z0, z1)) → add(active(z0), z1) 334.34/104.41
active(add(z0, z1)) → add(z0, active(z1)) 334.34/104.41
active(dbl(z0)) → dbl(active(z0)) 334.34/104.41
active(first(z0, z1)) → first(active(z0), z1) 334.34/104.41
active(first(z0, z1)) → first(z0, active(z1)) 334.34/104.41
terms(mark(z0)) → mark(terms(z0)) 334.34/104.41
terms(ok(z0)) → ok(terms(z0)) 334.34/104.41
cons(mark(z0), z1) → mark(cons(z0, z1)) 334.34/104.41
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 334.34/104.41
recip(mark(z0)) → mark(recip(z0)) 334.34/104.41
recip(ok(z0)) → ok(recip(z0)) 334.34/104.41
sqr(mark(z0)) → mark(sqr(z0)) 334.34/104.41
sqr(ok(z0)) → ok(sqr(z0)) 334.34/104.41
s(mark(z0)) → mark(s(z0)) 334.34/104.41
s(ok(z0)) → ok(s(z0)) 334.34/104.41
add(mark(z0), z1) → mark(add(z0, z1)) 334.34/104.41
add(z0, mark(z1)) → mark(add(z0, z1)) 334.34/104.41
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 334.34/104.41
dbl(mark(z0)) → mark(dbl(z0)) 334.34/104.41
dbl(ok(z0)) → ok(dbl(z0)) 334.34/104.41
first(mark(z0), z1) → mark(first(z0, z1)) 334.34/104.41
first(z0, mark(z1)) → mark(first(z0, z1)) 334.34/104.41
first(ok(z0), ok(z1)) → ok(first(z0, z1)) 334.34/104.41
proper(terms(z0)) → terms(proper(z0)) 334.34/104.41
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 334.34/104.41
proper(recip(z0)) → recip(proper(z0)) 334.34/104.41
proper(sqr(z0)) → sqr(proper(z0)) 334.34/104.41
proper(s(z0)) → s(proper(z0)) 334.34/104.41
proper(0) → ok(0) 334.34/104.41
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 334.34/104.41
proper(dbl(z0)) → dbl(proper(z0)) 334.34/104.41
proper(first(z0, z1)) → first(proper(z0), proper(z1)) 334.34/104.41
proper(nil) → ok(nil) 334.34/104.41
top(mark(z0)) → top(proper(z0)) 334.34/104.41
top(ok(z0)) → top(active(z0))

Tuples:

TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.41
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.41
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.41
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.41
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.41
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.41
SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.41
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.41
S(mark(z0)) → c27(S(z0)) 334.34/104.41
S(ok(z0)) → c28(S(z0)) 334.34/104.41
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.41
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.41
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.41
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.41
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.41
FIRST(mark(z0), z1) → c34(FIRST(z0, z1)) 334.34/104.41
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.41
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1))

S tuples:none
K tuples:

SQR(mark(z0)) → c25(SQR(z0)) 334.34/104.41
SQR(ok(z0)) → c26(SQR(z0)) 334.34/104.41
TERMS(mark(z0)) → c19(TERMS(z0)) 334.34/104.41
TERMS(ok(z0)) → c20(TERMS(z0)) 334.34/104.41
RECIP(mark(z0)) → c23(RECIP(z0)) 334.34/104.41
RECIP(ok(z0)) → c24(RECIP(z0)) 334.34/104.41
DBL(ok(z0)) → c33(DBL(z0)) 334.34/104.41
ADD(mark(z0), z1) → c29(ADD(z0, z1)) 334.34/104.41
DBL(mark(z0)) → c32(DBL(z0)) 334.34/104.41
CONS(ok(z0), ok(z1)) → c22(CONS(z0, z1)) 334.34/104.41
CONS(mark(z0), z1) → c21(CONS(z0, z1)) 334.34/104.41
S(mark(z0)) → c27(S(z0)) 334.34/104.41
S(ok(z0)) → c28(S(z0)) 334.34/104.41
FIRST(z0, mark(z1)) → c35(FIRST(z0, z1)) 334.34/104.41
FIRST(ok(z0), ok(z1)) → c36(FIRST(z0, z1)) 334.34/104.41
ADD(z0, mark(z1)) → c30(ADD(z0, z1)) 334.34/104.41
ADD(ok(z0), ok(z1)) → c31(ADD(z0, z1)) 334.34/104.41
FIRST(mark(z0), z1) → c34(FIRST(z0, z1))

Defined Rule Symbols:

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

Defined Pair Symbols:

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

Compound Symbols:

c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36

334.34/104.41

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

The set S is empty

334.34/104.41

(92) BOUNDS(O(1), O(1))

334.34/104.41