225.45/72.64 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml

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The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^3)).

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

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↳14 CdtProblem

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

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↳16 CdtProblem

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

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↳18 CdtProblem

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

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↳20 CdtProblem

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

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↳22 CdtProblem

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

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↳24 CdtProblem

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

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↳26 CdtProblem

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

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↳28 CdtProblem

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

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↳30 CdtProblem

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

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↳32 CdtProblem

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

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↳34 CdtProblem

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

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↳36 CdtProblem

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

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↳38 CdtProblem

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

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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 CdtUnreachableProof (⇔)

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↳44 CdtProblem

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

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↳46 CdtProblem

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

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↳48 CdtProblem

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↳49 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^3))))

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↳50 CdtProblem

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

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↳52 CdtProblem

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

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↳54 CdtProblem

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↳55 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))

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↳56 CdtProblem

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↳57 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^2))))

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↳58 CdtProblem

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

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↳60 CdtProblem

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

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↳62 CdtProblem

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

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↳64 CdtProblem

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

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↳66 CdtProblem

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

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↳68 BOUNDS(O(1), O(1))

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(0) Obligation:

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

active(fib(N)) → mark(sel(N, fib1(s(0), s(0)))) 225.83/72.71
active(fib1(X, Y)) → mark(cons(X, fib1(Y, add(X, Y)))) 225.83/72.71
active(add(0, X)) → mark(X) 225.83/72.71
active(add(s(X), Y)) → mark(s(add(X, Y))) 225.83/72.72
active(sel(0, cons(X, XS))) → mark(X) 225.83/72.72
active(sel(s(N), cons(X, XS))) → mark(sel(N, XS)) 225.83/72.72
active(fib(X)) → fib(active(X)) 225.83/72.72
active(sel(X1, X2)) → sel(active(X1), X2) 225.83/72.72
active(sel(X1, X2)) → sel(X1, active(X2)) 225.83/72.72
active(fib1(X1, X2)) → fib1(active(X1), X2) 225.83/72.72
active(fib1(X1, X2)) → fib1(X1, active(X2)) 225.83/72.72
active(s(X)) → s(active(X)) 225.83/72.72
active(cons(X1, X2)) → cons(active(X1), X2) 225.83/72.72
active(add(X1, X2)) → add(active(X1), X2) 225.83/72.72
active(add(X1, X2)) → add(X1, active(X2)) 225.83/72.72
fib(mark(X)) → mark(fib(X)) 225.83/72.72
sel(mark(X1), X2) → mark(sel(X1, X2)) 225.83/72.72
sel(X1, mark(X2)) → mark(sel(X1, X2)) 225.83/72.72
fib1(mark(X1), X2) → mark(fib1(X1, X2)) 225.83/72.72
fib1(X1, mark(X2)) → mark(fib1(X1, X2)) 225.83/72.72
s(mark(X)) → mark(s(X)) 225.83/72.72
cons(mark(X1), X2) → mark(cons(X1, X2)) 225.83/72.72
add(mark(X1), X2) → mark(add(X1, X2)) 225.83/72.72
add(X1, mark(X2)) → mark(add(X1, X2)) 225.83/72.72
proper(fib(X)) → fib(proper(X)) 225.83/72.72
proper(sel(X1, X2)) → sel(proper(X1), proper(X2)) 225.83/72.72
proper(fib1(X1, X2)) → fib1(proper(X1), proper(X2)) 225.83/72.72
proper(s(X)) → s(proper(X)) 225.83/72.72
proper(0) → ok(0) 225.83/72.72
proper(cons(X1, X2)) → cons(proper(X1), proper(X2)) 225.83/72.72
proper(add(X1, X2)) → add(proper(X1), proper(X2)) 225.83/72.72
fib(ok(X)) → ok(fib(X)) 225.83/72.72
sel(ok(X1), ok(X2)) → ok(sel(X1, X2)) 225.83/72.72
fib1(ok(X1), ok(X2)) → ok(fib1(X1, X2)) 225.83/72.72
s(ok(X)) → ok(s(X)) 225.83/72.72
cons(ok(X1), ok(X2)) → ok(cons(X1, X2)) 225.83/72.72
add(ok(X1), ok(X2)) → ok(add(X1, X2)) 225.83/72.72
top(mark(X)) → top(proper(X)) 225.83/72.72
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(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 225.83/72.72
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 225.83/72.72
active(add(0, z0)) → mark(z0) 225.83/72.72
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 225.83/72.72
active(sel(0, cons(z0, z1))) → mark(z0) 225.83/72.72
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 225.83/72.72
active(fib(z0)) → fib(active(z0)) 225.83/72.72
active(sel(z0, z1)) → sel(active(z0), z1) 225.83/72.72
active(sel(z0, z1)) → sel(z0, active(z1)) 225.83/72.72
active(fib1(z0, z1)) → fib1(active(z0), z1) 225.83/72.72
active(fib1(z0, z1)) → fib1(z0, active(z1)) 225.83/72.72
active(s(z0)) → s(active(z0)) 225.83/72.72
active(cons(z0, z1)) → cons(active(z0), z1) 225.83/72.72
active(add(z0, z1)) → add(active(z0), z1) 225.83/72.72
active(add(z0, z1)) → add(z0, active(z1)) 225.83/72.72
fib(mark(z0)) → mark(fib(z0)) 225.83/72.72
fib(ok(z0)) → ok(fib(z0)) 225.83/72.72
sel(mark(z0), z1) → mark(sel(z0, z1)) 225.83/72.72
sel(z0, mark(z1)) → mark(sel(z0, z1)) 225.83/72.72
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 225.83/72.72
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 225.83/72.72
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 225.83/72.72
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 225.83/72.72
s(mark(z0)) → mark(s(z0)) 225.83/72.72
s(ok(z0)) → ok(s(z0)) 225.83/72.72
cons(mark(z0), z1) → mark(cons(z0, z1)) 225.83/72.72
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 225.83/72.72
add(mark(z0), z1) → mark(add(z0, z1)) 225.83/72.72
add(z0, mark(z1)) → mark(add(z0, z1)) 225.83/72.72
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 225.83/72.72
proper(fib(z0)) → fib(proper(z0)) 225.83/72.72
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 225.83/72.72
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 225.83/72.72
proper(s(z0)) → s(proper(z0)) 225.83/72.72
proper(0) → ok(0) 225.83/72.72
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 225.83/72.72
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 225.83/72.72
top(mark(z0)) → top(proper(z0)) 225.83/72.72
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0)), S(0), S(0)) 225.83/72.72
ACTIVE(fib1(z0, z1)) → c1(CONS(z0, fib1(z1, add(z0, z1))), FIB1(z1, add(z0, z1)), ADD(z0, z1)) 225.83/72.72
ACTIVE(add(s(z0), z1)) → c3(S(add(z0, z1)), ADD(z0, z1)) 225.83/72.72
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 225.83/72.72
ACTIVE(fib(z0)) → c6(FIB(active(z0)), ACTIVE(z0)) 225.83/72.72
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 225.83/72.72
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 225.83/72.72
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 225.83/72.72
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 225.83/72.72
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 225.83/72.72
ACTIVE(cons(z0, z1)) → c12(CONS(active(z0), z1), ACTIVE(z0)) 225.83/72.72
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 225.83/72.72
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 225.83/72.72
FIB(mark(z0)) → c15(FIB(z0)) 225.83/72.72
FIB(ok(z0)) → c16(FIB(z0)) 225.83/72.72
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 225.83/72.72
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 225.83/72.72
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 225.83/72.72
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 225.83/72.72
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 225.83/72.72
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 225.83/72.72
S(mark(z0)) → c23(S(z0)) 225.83/72.72
S(ok(z0)) → c24(S(z0)) 225.83/72.72
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 225.83/72.72
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 225.83/72.72
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 225.83/72.72
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 225.83/72.72
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 225.83/72.72
PROPER(fib(z0)) → c30(FIB(proper(z0)), PROPER(z0)) 225.83/72.72
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 225.83/72.72
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 225.83/72.72
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 225.83/72.72
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 225.83/72.72
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 225.83/72.72
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 225.83/72.72
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0))

S tuples:

ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0))), FIB1(s(0), s(0)), S(0), S(0)) 225.83/72.72
ACTIVE(fib1(z0, z1)) → c1(CONS(z0, fib1(z1, add(z0, z1))), FIB1(z1, add(z0, z1)), ADD(z0, z1)) 225.83/72.72
ACTIVE(add(s(z0), z1)) → c3(S(add(z0, z1)), ADD(z0, z1)) 225.83/72.72
ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 225.83/72.72
ACTIVE(fib(z0)) → c6(FIB(active(z0)), ACTIVE(z0)) 225.83/72.72
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 225.83/72.72
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 225.83/72.72
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 225.83/72.72
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 225.83/72.72
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 225.83/72.72
ACTIVE(cons(z0, z1)) → c12(CONS(active(z0), z1), ACTIVE(z0)) 225.83/72.72
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 225.83/72.72
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 225.83/72.72
FIB(mark(z0)) → c15(FIB(z0)) 225.83/72.72
FIB(ok(z0)) → c16(FIB(z0)) 225.83/72.72
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.84
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.84
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.84
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.84
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.84
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.84
S(mark(z0)) → c23(S(z0)) 226.18/72.84
S(ok(z0)) → c24(S(z0)) 226.18/72.84
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.84
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.84
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.84
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.84
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.84
PROPER(fib(z0)) → c30(FIB(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.84
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c, c1, c3, c5, c6, c7, 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, c35, c36, c37, c38

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

Removed 6 trailing tuple parts

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(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.84
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.84
active(add(0, z0)) → mark(z0) 226.18/72.84
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.84
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.84
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.84
active(fib(z0)) → fib(active(z0)) 226.18/72.84
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.84
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.84
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.84
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.84
active(s(z0)) → s(active(z0)) 226.18/72.84
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.84
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.84
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.84
fib(mark(z0)) → mark(fib(z0)) 226.18/72.84
fib(ok(z0)) → ok(fib(z0)) 226.18/72.84
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.84
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.84
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.84
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.84
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.84
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.84
s(mark(z0)) → mark(s(z0)) 226.18/72.84
s(ok(z0)) → ok(s(z0)) 226.18/72.84
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.84
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.84
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.84
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.84
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.84
proper(fib(z0)) → fib(proper(z0)) 226.18/72.84
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.84
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.84
proper(s(z0)) → s(proper(z0)) 226.18/72.84
proper(0) → ok(0) 226.18/72.84
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.84
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.84
top(mark(z0)) → top(proper(z0)) 226.18/72.84
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.84
ACTIVE(fib(z0)) → c6(FIB(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(cons(z0, z1)) → c12(CONS(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.84
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.84
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.84
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.84
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.84
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.84
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.84
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.84
S(mark(z0)) → c23(S(z0)) 226.18/72.84
S(ok(z0)) → c24(S(z0)) 226.18/72.84
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.84
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.84
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.84
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.84
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.84
PROPER(fib(z0)) → c30(FIB(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.84
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.84
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.84
ACTIVE(fib(z0)) → c6(FIB(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(cons(z0, z1)) → c12(CONS(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.84
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.84
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.84
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.84
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.84
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.84
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.84
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.84
S(mark(z0)) → c23(S(z0)) 226.18/72.84
S(ok(z0)) → c24(S(z0)) 226.18/72.84
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.84
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.84
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.84
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.84
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.84
PROPER(fib(z0)) → c30(FIB(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.84
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.84
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c6, c7, 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, c35, c36, c37, c38, c, c1, c3

226.18/72.84

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

Use narrowing to replace ACTIVE(fib(z0)) → c6(FIB(active(z0)), ACTIVE(z0)) by

ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.84
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.84
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.84
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.84
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.84
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.84
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.84
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1)))

226.18/72.84

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.84
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.84
active(add(0, z0)) → mark(z0) 226.18/72.84
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.84
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.84
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.84
active(fib(z0)) → fib(active(z0)) 226.18/72.84
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.84
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.84
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.84
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.84
active(s(z0)) → s(active(z0)) 226.18/72.84
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.84
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.84
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.84
fib(mark(z0)) → mark(fib(z0)) 226.18/72.84
fib(ok(z0)) → ok(fib(z0)) 226.18/72.84
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.84
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.84
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.84
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.84
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.84
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.84
s(mark(z0)) → mark(s(z0)) 226.18/72.84
s(ok(z0)) → ok(s(z0)) 226.18/72.84
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.84
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.84
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.84
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.84
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.84
proper(fib(z0)) → fib(proper(z0)) 226.18/72.84
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.84
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.84
proper(s(z0)) → s(proper(z0)) 226.18/72.84
proper(0) → ok(0) 226.18/72.84
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.84
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.84
top(mark(z0)) → top(proper(z0)) 226.18/72.84
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(cons(z0, z1)) → c12(CONS(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.84
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.84
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.84
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.84
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.84
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.84
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.84
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.84
S(mark(z0)) → c23(S(z0)) 226.18/72.84
S(ok(z0)) → c24(S(z0)) 226.18/72.84
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.84
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.84
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.84
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.84
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.84
PROPER(fib(z0)) → c30(FIB(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.84
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.84
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.84
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.84
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.84
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.84
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.84
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.84
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.84
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.84
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1)))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(cons(z0, z1)) → c12(CONS(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.84
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.84
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.84
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.84
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.84
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.84
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.84
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.84
S(mark(z0)) → c23(S(z0)) 226.18/72.84
S(ok(z0)) → c24(S(z0)) 226.18/72.84
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.84
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.84
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.84
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.84
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.84
PROPER(fib(z0)) → c30(FIB(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.84
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.84
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.84
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.84
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.84
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.84
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.84
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.84
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.84
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.84
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1)))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, 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, c35, c36, c37, c38, c, c1, c3, c6

226.18/72.84

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

Use narrowing to replace ACTIVE(s(z0)) → c11(S(active(z0)), ACTIVE(z0)) by

ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.84
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.84
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.84
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.84
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.84
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.84
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.84
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))

226.18/72.84

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.84
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.84
active(add(0, z0)) → mark(z0) 226.18/72.84
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.84
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.84
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.84
active(fib(z0)) → fib(active(z0)) 226.18/72.84
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.84
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.84
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.84
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.84
active(s(z0)) → s(active(z0)) 226.18/72.84
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.84
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.84
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.84
fib(mark(z0)) → mark(fib(z0)) 226.18/72.84
fib(ok(z0)) → ok(fib(z0)) 226.18/72.84
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.84
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.84
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.84
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.84
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.84
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.84
s(mark(z0)) → mark(s(z0)) 226.18/72.84
s(ok(z0)) → ok(s(z0)) 226.18/72.84
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.84
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.84
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.84
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.84
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.84
proper(fib(z0)) → fib(proper(z0)) 226.18/72.84
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.84
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.84
proper(s(z0)) → s(proper(z0)) 226.18/72.84
proper(0) → ok(0) 226.18/72.84
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.84
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.84
top(mark(z0)) → top(proper(z0)) 226.18/72.84
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(cons(z0, z1)) → c12(CONS(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.84
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.84
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.84
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.84
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.84
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.84
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.84
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.84
S(mark(z0)) → c23(S(z0)) 226.18/72.84
S(ok(z0)) → c24(S(z0)) 226.18/72.84
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.84
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.84
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.84
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.84
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.84
PROPER(fib(z0)) → c30(FIB(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.84
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.84
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.84
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.84
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.84
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.84
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.84
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.84
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.84
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.84
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.84
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.84
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.84
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.84
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.84
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.84
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.84
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.84
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
ACTIVE(cons(z0, z1)) → c12(CONS(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.84
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.84
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.84
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.84
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.84
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.84
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.84
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.84
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.84
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.84
S(mark(z0)) → c23(S(z0)) 226.18/72.84
S(ok(z0)) → c24(S(z0)) 226.18/72.84
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.84
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.84
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.84
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.84
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.84
PROPER(fib(z0)) → c30(FIB(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.84
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.84
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.84
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.84
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.84
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.84
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.84
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.84
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.84
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.84
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.84
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.84
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.84
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.84
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.84
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.84
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.84
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.84
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.84
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.84
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.84
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.84
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1)))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c, c1, c3, c6, c11

226.18/72.84

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

Use narrowing to replace ACTIVE(cons(z0, z1)) → c12(CONS(active(z0), z1), ACTIVE(z0)) by

ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.84
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.84
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.84
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.84
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.84
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.84
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.84
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.84
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.84
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.84
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))

226.18/72.84

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.84
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.84
active(add(0, z0)) → mark(z0) 226.18/72.84
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.84
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.84
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.84
active(fib(z0)) → fib(active(z0)) 226.18/72.84
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.84
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.84
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.84
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.84
active(s(z0)) → s(active(z0)) 226.18/72.84
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.84
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.84
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.84
fib(mark(z0)) → mark(fib(z0)) 226.18/72.84
fib(ok(z0)) → ok(fib(z0)) 226.18/72.84
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.84
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.84
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.84
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.85
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.85
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.85
s(mark(z0)) → mark(s(z0)) 226.18/72.85
s(ok(z0)) → ok(s(z0)) 226.18/72.85
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.85
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.85
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.85
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.85
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.85
proper(fib(z0)) → fib(proper(z0)) 226.18/72.85
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.85
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.85
proper(s(z0)) → s(proper(z0)) 226.18/72.85
proper(0) → ok(0) 226.18/72.85
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.85
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.85
top(mark(z0)) → top(proper(z0)) 226.18/72.85
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(fib(z0)) → c30(FIB(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(fib(z0)) → c30(FIB(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1)))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c35, c36, c37, c38, c, c1, c3, c6, c11, c12

226.18/72.85

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

Use narrowing to replace PROPER(fib(z0)) → c30(FIB(proper(z0)), PROPER(z0)) by

PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.85
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.85
PROPER(fib(0)) → c30(FIB(ok(0)), PROPER(0)) 226.18/72.85
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))

226.18/72.85

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.85
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.85
active(add(0, z0)) → mark(z0) 226.18/72.85
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.85
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.85
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.85
active(fib(z0)) → fib(active(z0)) 226.18/72.85
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.85
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.85
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.85
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.85
active(s(z0)) → s(active(z0)) 226.18/72.85
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.85
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.85
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.85
fib(mark(z0)) → mark(fib(z0)) 226.18/72.85
fib(ok(z0)) → ok(fib(z0)) 226.18/72.85
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.85
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.85
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.85
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.85
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.85
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.85
s(mark(z0)) → mark(s(z0)) 226.18/72.85
s(ok(z0)) → ok(s(z0)) 226.18/72.85
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.85
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.85
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.85
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.85
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.85
proper(fib(z0)) → fib(proper(z0)) 226.18/72.85
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.85
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.85
proper(s(z0)) → s(proper(z0)) 226.18/72.85
proper(0) → ok(0) 226.18/72.85
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.85
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.85
top(mark(z0)) → top(proper(z0)) 226.18/72.85
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.85
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.85
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.85
PROPER(fib(0)) → c30(FIB(ok(0)), PROPER(0)) 226.18/72.85
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.85
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.85
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.85
PROPER(fib(0)) → c30(FIB(ok(0)), PROPER(0)) 226.18/72.85
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c31, c32, c33, c35, c36, c37, c38, c, c1, c3, c6, c11, c12, c30

226.18/72.85

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

Removed 1 trailing tuple parts

226.18/72.85

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.85
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.85
active(add(0, z0)) → mark(z0) 226.18/72.85
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.85
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.85
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.85
active(fib(z0)) → fib(active(z0)) 226.18/72.85
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.85
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.85
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.85
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.85
active(s(z0)) → s(active(z0)) 226.18/72.85
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.85
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.85
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.85
fib(mark(z0)) → mark(fib(z0)) 226.18/72.85
fib(ok(z0)) → ok(fib(z0)) 226.18/72.85
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.85
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.85
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.85
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.85
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.85
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.85
s(mark(z0)) → mark(s(z0)) 226.18/72.85
s(ok(z0)) → ok(s(z0)) 226.18/72.85
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.85
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.85
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.85
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.85
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.85
proper(fib(z0)) → fib(proper(z0)) 226.18/72.85
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.85
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.85
proper(s(z0)) → s(proper(z0)) 226.18/72.85
proper(0) → ok(0) 226.18/72.85
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.85
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.85
top(mark(z0)) → top(proper(z0)) 226.18/72.85
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.85
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.85
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.85
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.85
PROPER(fib(0)) → c30(FIB(ok(0)))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.85
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.85
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.85
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.85
PROPER(fib(0)) → c30(FIB(ok(0)))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c31, c32, c33, c35, c36, c37, c38, c, c1, c3, c6, c11, c12, c30, c30

226.18/72.85

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

Use narrowing to replace PROPER(sel(z0, z1)) → c31(SEL(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.85
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.85
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.85
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.85
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.85
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

226.18/72.85

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.85
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.85
active(add(0, z0)) → mark(z0) 226.18/72.85
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.85
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.85
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.85
active(fib(z0)) → fib(active(z0)) 226.18/72.85
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.85
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.85
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.85
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.85
active(s(z0)) → s(active(z0)) 226.18/72.85
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.85
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.85
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.85
fib(mark(z0)) → mark(fib(z0)) 226.18/72.85
fib(ok(z0)) → ok(fib(z0)) 226.18/72.85
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.85
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.85
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.85
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.85
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.85
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.85
s(mark(z0)) → mark(s(z0)) 226.18/72.85
s(ok(z0)) → ok(s(z0)) 226.18/72.85
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.85
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.85
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.85
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.85
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.85
proper(fib(z0)) → fib(proper(z0)) 226.18/72.85
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.85
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.85
proper(s(z0)) → s(proper(z0)) 226.18/72.85
proper(0) → ok(0) 226.18/72.85
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.85
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.85
top(mark(z0)) → top(proper(z0)) 226.18/72.85
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.85
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.85
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.85
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.85
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.85
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.85
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.85
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.85
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.85
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.85
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.85
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.85
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.85
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.85
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.85
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.85
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.85
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.85
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.85
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.85
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c32, c33, c35, c36, c37, c38, c, c1, c3, c6, c11, c12, c30, c30, c31

226.18/72.85

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

Removed 2 trailing tuple parts

226.18/72.85

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.85
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.85
active(add(0, z0)) → mark(z0) 226.18/72.85
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.85
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.85
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.85
active(fib(z0)) → fib(active(z0)) 226.18/72.85
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.85
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.85
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.85
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.85
active(s(z0)) → s(active(z0)) 226.18/72.85
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.85
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.85
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.85
fib(mark(z0)) → mark(fib(z0)) 226.18/72.85
fib(ok(z0)) → ok(fib(z0)) 226.18/72.85
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.85
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.85
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.85
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.85
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.85
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.85
s(mark(z0)) → mark(s(z0)) 226.18/72.85
s(ok(z0)) → ok(s(z0)) 226.18/72.85
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.85
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.85
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.85
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.85
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.85
proper(fib(z0)) → fib(proper(z0)) 226.18/72.85
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.85
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.85
proper(s(z0)) → s(proper(z0)) 226.18/72.85
proper(0) → ok(0) 226.18/72.85
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.85
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.85
top(mark(z0)) → top(proper(z0)) 226.18/72.85
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.85
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.85
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.85
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.85
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.85
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.85
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.85
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.85
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.85
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.85
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.85
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.85
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.85
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.85
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.85
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.85
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.85
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.85
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c32, c33, c35, c36, c37, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31

226.18/72.85

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

Use narrowing to replace PROPER(fib1(z0, z1)) → c32(FIB1(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.85
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.85
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.85
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.85
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.85
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.85
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.85
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

226.18/72.85

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.85
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.85
active(add(0, z0)) → mark(z0) 226.18/72.85
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.85
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.85
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.85
active(fib(z0)) → fib(active(z0)) 226.18/72.85
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.85
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.85
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.85
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.85
active(s(z0)) → s(active(z0)) 226.18/72.85
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.85
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.85
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.85
fib(mark(z0)) → mark(fib(z0)) 226.18/72.85
fib(ok(z0)) → ok(fib(z0)) 226.18/72.85
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.85
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.85
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.85
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.85
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.85
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.85
s(mark(z0)) → mark(s(z0)) 226.18/72.85
s(ok(z0)) → ok(s(z0)) 226.18/72.85
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.85
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.85
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.85
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.85
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.85
proper(fib(z0)) → fib(proper(z0)) 226.18/72.85
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.85
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.85
proper(s(z0)) → s(proper(z0)) 226.18/72.85
proper(0) → ok(0) 226.18/72.85
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.85
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.85
top(mark(z0)) → top(proper(z0)) 226.18/72.85
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.85
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.85
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.85
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.85
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.85
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.85
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.85
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.85
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.85
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.85
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.85
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.85
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.85
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.85
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.85
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.85
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.85
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.85
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.85
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.85
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.85
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.85
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.85
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.85
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.85
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.85
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.85
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.85
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.85
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.85
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.85
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.85
S(mark(z0)) → c23(S(z0)) 226.18/72.85
S(ok(z0)) → c24(S(z0)) 226.18/72.85
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.85
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.85
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.85
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.85
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.85
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.85
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.85
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.85
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.85
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.85
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.85
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.85
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.85
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.85
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.85
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.85
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.85
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.85
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.86
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.86
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.86
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.86
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c33, c35, c36, c37, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32

226.18/72.86

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

Removed 2 trailing tuple parts

226.18/72.86

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.86
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.86
active(add(0, z0)) → mark(z0) 226.18/72.86
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.86
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.86
active(fib(z0)) → fib(active(z0)) 226.18/72.86
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.86
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.86
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.86
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.86
active(s(z0)) → s(active(z0)) 226.18/72.86
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.86
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.86
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.86
fib(mark(z0)) → mark(fib(z0)) 226.18/72.86
fib(ok(z0)) → ok(fib(z0)) 226.18/72.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.86
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.86
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.86
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.86
s(mark(z0)) → mark(s(z0)) 226.18/72.86
s(ok(z0)) → ok(s(z0)) 226.18/72.86
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.86
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.86
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.86
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.86
proper(fib(z0)) → fib(proper(z0)) 226.18/72.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.86
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.86
proper(s(z0)) → s(proper(z0)) 226.18/72.86
proper(0) → ok(0) 226.18/72.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.86
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.86
top(mark(z0)) → top(proper(z0)) 226.18/72.86
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.86
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.86
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.86
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.86
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.86
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.86
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.86
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.86
S(mark(z0)) → c23(S(z0)) 226.18/72.86
S(ok(z0)) → c24(S(z0)) 226.18/72.86
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.86
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.86
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.86
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.86
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.86
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.86
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.86
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.86
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.86
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.86
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.86
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.86
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.86
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.86
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.86
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.86
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.86
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.86
S(mark(z0)) → c23(S(z0)) 226.18/72.86
S(ok(z0)) → c24(S(z0)) 226.18/72.86
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.86
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.86
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.86
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.86
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.86
PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) 226.18/72.86
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.86
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.86
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.86
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.86
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c33, c35, c36, c37, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32, c32

226.18/72.86

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

Use narrowing to replace PROPER(s(z0)) → c33(S(proper(z0)), PROPER(z0)) by

PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(s(0)) → c33(S(ok(0)), PROPER(0)) 226.18/72.86
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))

226.18/72.86

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.86
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.86
active(add(0, z0)) → mark(z0) 226.18/72.86
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.86
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.86
active(fib(z0)) → fib(active(z0)) 226.18/72.86
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.86
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.86
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.86
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.86
active(s(z0)) → s(active(z0)) 226.18/72.86
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.86
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.86
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.86
fib(mark(z0)) → mark(fib(z0)) 226.18/72.86
fib(ok(z0)) → ok(fib(z0)) 226.18/72.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.86
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.86
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.86
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.86
s(mark(z0)) → mark(s(z0)) 226.18/72.86
s(ok(z0)) → ok(s(z0)) 226.18/72.86
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.86
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.86
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.86
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.86
proper(fib(z0)) → fib(proper(z0)) 226.18/72.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.86
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.86
proper(s(z0)) → s(proper(z0)) 226.18/72.86
proper(0) → ok(0) 226.18/72.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.86
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.86
top(mark(z0)) → top(proper(z0)) 226.18/72.86
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.86
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.86
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.86
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.86
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.86
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.86
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.86
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.86
S(mark(z0)) → c23(S(z0)) 226.18/72.86
S(ok(z0)) → c24(S(z0)) 226.18/72.86
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.86
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.86
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.86
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.86
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.86
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.86
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.86
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.86
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.86
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(s(0)) → c33(S(ok(0)), PROPER(0)) 226.18/72.86
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.86
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.86
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.86
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.86
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.86
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.86
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.86
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.86
S(mark(z0)) → c23(S(z0)) 226.18/72.86
S(ok(z0)) → c24(S(z0)) 226.18/72.86
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.86
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.86
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.86
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.86
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.86
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.86
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.86
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.86
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.86
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(s(0)) → c33(S(ok(0)), PROPER(0)) 226.18/72.86
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c35, c36, c37, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32, c32, c33

226.18/72.86

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

Removed 1 trailing tuple parts

226.18/72.86

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.86
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.86
active(add(0, z0)) → mark(z0) 226.18/72.86
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.86
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.86
active(fib(z0)) → fib(active(z0)) 226.18/72.86
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.86
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.86
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.86
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.86
active(s(z0)) → s(active(z0)) 226.18/72.86
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.86
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.86
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.86
fib(mark(z0)) → mark(fib(z0)) 226.18/72.86
fib(ok(z0)) → ok(fib(z0)) 226.18/72.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.86
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.86
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.86
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.86
s(mark(z0)) → mark(s(z0)) 226.18/72.86
s(ok(z0)) → ok(s(z0)) 226.18/72.86
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.86
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.86
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.86
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.86
proper(fib(z0)) → fib(proper(z0)) 226.18/72.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.86
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.86
proper(s(z0)) → s(proper(z0)) 226.18/72.86
proper(0) → ok(0) 226.18/72.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.86
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.86
top(mark(z0)) → top(proper(z0)) 226.18/72.86
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.86
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.86
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.86
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.86
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.86
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.86
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.86
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.86
S(mark(z0)) → c23(S(z0)) 226.18/72.86
S(ok(z0)) → c24(S(z0)) 226.18/72.86
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.86
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.86
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.86
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.86
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.86
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.86
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.86
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.86
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.86
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(s(0)) → c33(S(ok(0)))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.86
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.86
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.86
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.86
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.86
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.86
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.86
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.86
S(mark(z0)) → c23(S(z0)) 226.18/72.86
S(ok(z0)) → c24(S(z0)) 226.18/72.86
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.86
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.86
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.86
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.86
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.86
PROPER(cons(z0, z1)) → c35(CONS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.86
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.86
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.86
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.86
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(s(0)) → c33(S(ok(0)))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c35, c36, c37, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32, c32, c33, c33

226.18/72.86

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

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

PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.86
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.86
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

226.18/72.86

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.86
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.86
active(add(0, z0)) → mark(z0) 226.18/72.86
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.86
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.86
active(fib(z0)) → fib(active(z0)) 226.18/72.86
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.86
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.86
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.86
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.86
active(s(z0)) → s(active(z0)) 226.18/72.86
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.86
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.86
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.86
fib(mark(z0)) → mark(fib(z0)) 226.18/72.86
fib(ok(z0)) → ok(fib(z0)) 226.18/72.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.86
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.86
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.86
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.86
s(mark(z0)) → mark(s(z0)) 226.18/72.86
s(ok(z0)) → ok(s(z0)) 226.18/72.86
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.86
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.86
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.86
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.86
proper(fib(z0)) → fib(proper(z0)) 226.18/72.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.86
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.86
proper(s(z0)) → s(proper(z0)) 226.18/72.86
proper(0) → ok(0) 226.18/72.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.86
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.86
top(mark(z0)) → top(proper(z0)) 226.18/72.86
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.86
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.86
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.86
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.86
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.86
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.86
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.86
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.86
S(mark(z0)) → c23(S(z0)) 226.18/72.86
S(ok(z0)) → c24(S(z0)) 226.18/72.86
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.86
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.86
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.86
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.86
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.86
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.86
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.86
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.86
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.86
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.86
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.86
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.86
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.86
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.86
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.86
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.86
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.86
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.86
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.86
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.86
S(mark(z0)) → c23(S(z0)) 226.18/72.86
S(ok(z0)) → c24(S(z0)) 226.18/72.86
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.86
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.86
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.86
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.86
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.86
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.86
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.86
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.86
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.86
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.86
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.86
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.86
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c36, c37, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32, c32, c33, c33, c35

226.18/72.86

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

Removed 2 trailing tuple parts

226.18/72.86

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.86
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.86
active(add(0, z0)) → mark(z0) 226.18/72.86
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.86
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.86
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.86
active(fib(z0)) → fib(active(z0)) 226.18/72.86
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.86
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.86
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.86
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.86
active(s(z0)) → s(active(z0)) 226.18/72.86
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.86
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.86
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.86
fib(mark(z0)) → mark(fib(z0)) 226.18/72.86
fib(ok(z0)) → ok(fib(z0)) 226.18/72.86
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.86
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.86
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.86
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.86
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.86
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.86
s(mark(z0)) → mark(s(z0)) 226.18/72.86
s(ok(z0)) → ok(s(z0)) 226.18/72.86
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.86
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.86
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.86
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.86
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.86
proper(fib(z0)) → fib(proper(z0)) 226.18/72.86
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.86
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.86
proper(s(z0)) → s(proper(z0)) 226.18/72.86
proper(0) → ok(0) 226.18/72.86
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.86
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.86
top(mark(z0)) → top(proper(z0)) 226.18/72.86
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.86
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.86
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.86
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.86
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.86
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.86
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.86
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.86
S(mark(z0)) → c23(S(z0)) 226.18/72.86
S(ok(z0)) → c24(S(z0)) 226.18/72.86
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.86
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.86
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.86
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.86
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.86
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.86
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.86
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.86
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.86
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.86
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.86
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.86
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.86
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.86
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.86
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.86
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.86
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.86
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.86
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.86
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.86
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.86
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.86
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.86
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.86
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.86
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.86
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.86
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.86
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.86
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.86
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.86
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.86
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.86
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.86
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.86
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.86
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.86
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.86
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.86
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.86
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.86
S(mark(z0)) → c23(S(z0)) 226.18/72.87
S(ok(z0)) → c24(S(z0)) 226.18/72.87
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.87
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.87
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.87
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.87
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.87
PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 226.18/72.87
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.87
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.87
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.87
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.87
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.87
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c36, c37, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32, c32, c33, c33, c35, c35

226.18/72.87

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

Use narrowing to replace PROPER(add(z0, z1)) → c36(ADD(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.87
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.87
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

226.18/72.87

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.87
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.87
active(add(0, z0)) → mark(z0) 226.18/72.87
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.87
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.87
active(fib(z0)) → fib(active(z0)) 226.18/72.87
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.87
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.87
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.87
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.87
active(s(z0)) → s(active(z0)) 226.18/72.87
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.87
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.87
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.87
fib(mark(z0)) → mark(fib(z0)) 226.18/72.87
fib(ok(z0)) → ok(fib(z0)) 226.18/72.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.87
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.87
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.87
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.87
s(mark(z0)) → mark(s(z0)) 226.18/72.87
s(ok(z0)) → ok(s(z0)) 226.18/72.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.87
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.87
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.87
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.87
proper(fib(z0)) → fib(proper(z0)) 226.18/72.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.87
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.87
proper(s(z0)) → s(proper(z0)) 226.18/72.87
proper(0) → ok(0) 226.18/72.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.87
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.87
top(mark(z0)) → top(proper(z0)) 226.18/72.87
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.87
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.87
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.87
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.87
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.87
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.87
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.87
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.87
S(mark(z0)) → c23(S(z0)) 226.18/72.87
S(ok(z0)) → c24(S(z0)) 226.18/72.87
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.87
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.87
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.87
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.87
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.87
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.87
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.87
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.87
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.87
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.87
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.87
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.87
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.87
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.87
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.87
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.87
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.87
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.87
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.87
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.87
S(mark(z0)) → c23(S(z0)) 226.18/72.87
S(ok(z0)) → c24(S(z0)) 226.18/72.87
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.87
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.87
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.87
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.87
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.87
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.87
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.87
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.87
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.87
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.87
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 226.18/72.87
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(0), PROPER(x1)) 226.18/72.87
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, TOP, PROPER

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c37, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32, c32, c33, c33, c35, c35, c36

226.18/72.87

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

Removed 2 trailing tuple parts

226.18/72.87

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.87
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.87
active(add(0, z0)) → mark(z0) 226.18/72.87
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.87
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.87
active(fib(z0)) → fib(active(z0)) 226.18/72.87
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.87
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.87
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.87
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.87
active(s(z0)) → s(active(z0)) 226.18/72.87
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.87
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.87
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.87
fib(mark(z0)) → mark(fib(z0)) 226.18/72.87
fib(ok(z0)) → ok(fib(z0)) 226.18/72.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.87
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.87
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.87
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.87
s(mark(z0)) → mark(s(z0)) 226.18/72.87
s(ok(z0)) → ok(s(z0)) 226.18/72.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.87
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.87
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.87
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.87
proper(fib(z0)) → fib(proper(z0)) 226.18/72.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.87
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.87
proper(s(z0)) → s(proper(z0)) 226.18/72.87
proper(0) → ok(0) 226.18/72.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.87
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.87
top(mark(z0)) → top(proper(z0)) 226.18/72.87
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.87
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.87
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.87
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.87
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.87
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.87
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.87
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.87
S(mark(z0)) → c23(S(z0)) 226.18/72.87
S(ok(z0)) → c24(S(z0)) 226.18/72.87
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.87
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.87
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.87
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.87
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.87
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.87
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.87
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.87
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.87
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.87
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.87
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.87
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.87
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.87
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.87
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.87
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.87
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.87
S(mark(z0)) → c23(S(z0)) 226.18/72.87
S(ok(z0)) → c24(S(z0)) 226.18/72.87
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.87
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.87
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.87
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.87
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.87
TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) 226.18/72.87
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.87
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.87
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.87
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.87
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, TOP, PROPER

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c37, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32, c32, c33, c33, c35, c35, c36, c36

226.18/72.87

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

Use narrowing to replace TOP(mark(z0)) → c37(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(fib(z0))) → c37(TOP(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
TOP(mark(sel(z0, z1))) → c37(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
TOP(mark(fib1(z0, z1))) → c37(TOP(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
TOP(mark(s(z0))) → c37(TOP(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
TOP(mark(0)) → c37(TOP(ok(0)), PROPER(0)) 226.18/72.87
TOP(mark(cons(z0, z1))) → c37(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
TOP(mark(add(z0, z1))) → c37(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))

226.18/72.87

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.87
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.87
active(add(0, z0)) → mark(z0) 226.18/72.87
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.87
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.87
active(fib(z0)) → fib(active(z0)) 226.18/72.87
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.87
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.87
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.87
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.87
active(s(z0)) → s(active(z0)) 226.18/72.87
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.87
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.87
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.87
fib(mark(z0)) → mark(fib(z0)) 226.18/72.87
fib(ok(z0)) → ok(fib(z0)) 226.18/72.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.87
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.87
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.87
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.87
s(mark(z0)) → mark(s(z0)) 226.18/72.87
s(ok(z0)) → ok(s(z0)) 226.18/72.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.87
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.87
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.87
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.87
proper(fib(z0)) → fib(proper(z0)) 226.18/72.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.87
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.87
proper(s(z0)) → s(proper(z0)) 226.18/72.87
proper(0) → ok(0) 226.18/72.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.87
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.87
top(mark(z0)) → top(proper(z0)) 226.18/72.87
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.87
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.87
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.87
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.87
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.87
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.87
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.87
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.87
S(mark(z0)) → c23(S(z0)) 226.18/72.87
S(ok(z0)) → c24(S(z0)) 226.18/72.87
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.87
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.87
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.87
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.87
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.87
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.87
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.87
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.87
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.87
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
TOP(mark(fib(z0))) → c37(TOP(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
TOP(mark(sel(z0, z1))) → c37(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
TOP(mark(fib1(z0, z1))) → c37(TOP(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
TOP(mark(s(z0))) → c37(TOP(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
TOP(mark(0)) → c37(TOP(ok(0)), PROPER(0)) 226.18/72.87
TOP(mark(cons(z0, z1))) → c37(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
TOP(mark(add(z0, z1))) → c37(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.87
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.87
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.87
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.87
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.87
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.87
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.87
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.87
S(mark(z0)) → c23(S(z0)) 226.18/72.87
S(ok(z0)) → c24(S(z0)) 226.18/72.87
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.87
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.87
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.87
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.87
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.87
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.87
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.87
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.87
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.87
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
TOP(mark(fib(z0))) → c37(TOP(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
TOP(mark(sel(z0, z1))) → c37(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
TOP(mark(fib1(z0, z1))) → c37(TOP(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
TOP(mark(s(z0))) → c37(TOP(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
TOP(mark(0)) → c37(TOP(ok(0)), PROPER(0)) 226.18/72.87
TOP(mark(cons(z0, z1))) → c37(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
TOP(mark(add(z0, z1))) → c37(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, TOP, PROPER

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32, c32, c33, c33, c35, c35, c36, c36, c37

226.18/72.87

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

Removed 1 trailing tuple parts

226.18/72.87

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.87
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.87
active(add(0, z0)) → mark(z0) 226.18/72.87
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.87
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.87
active(fib(z0)) → fib(active(z0)) 226.18/72.87
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.87
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.87
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.87
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.87
active(s(z0)) → s(active(z0)) 226.18/72.87
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.87
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.87
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.87
fib(mark(z0)) → mark(fib(z0)) 226.18/72.87
fib(ok(z0)) → ok(fib(z0)) 226.18/72.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.87
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.87
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.87
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.87
s(mark(z0)) → mark(s(z0)) 226.18/72.87
s(ok(z0)) → ok(s(z0)) 226.18/72.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.87
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.87
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.87
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.87
proper(fib(z0)) → fib(proper(z0)) 226.18/72.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.87
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.87
proper(s(z0)) → s(proper(z0)) 226.18/72.87
proper(0) → ok(0) 226.18/72.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.87
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.87
top(mark(z0)) → top(proper(z0)) 226.18/72.87
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.87
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.87
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.87
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.87
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.87
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.87
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.87
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.87
S(mark(z0)) → c23(S(z0)) 226.18/72.87
S(ok(z0)) → c24(S(z0)) 226.18/72.87
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.87
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.87
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.87
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.87
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.87
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.87
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.87
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.87
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.87
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
TOP(mark(fib(z0))) → c37(TOP(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
TOP(mark(sel(z0, z1))) → c37(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
TOP(mark(fib1(z0, z1))) → c37(TOP(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
TOP(mark(s(z0))) → c37(TOP(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
TOP(mark(cons(z0, z1))) → c37(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
TOP(mark(add(z0, z1))) → c37(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
TOP(mark(0)) → c37(TOP(ok(0)))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.87
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.87
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.87
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.87
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.87
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.87
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.87
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.87
S(mark(z0)) → c23(S(z0)) 226.18/72.87
S(ok(z0)) → c24(S(z0)) 226.18/72.87
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.87
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.87
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.87
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.87
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.87
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.87
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.87
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.87
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.87
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.87
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.87
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.87
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.87
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.87
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.87
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.87
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.87
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.87
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.87
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.87
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.87
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.87
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.87
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.87
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.87
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1)) 226.18/72.87
TOP(mark(fib(z0))) → c37(TOP(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.87
TOP(mark(sel(z0, z1))) → c37(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.87
TOP(mark(fib1(z0, z1))) → c37(TOP(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.87
TOP(mark(s(z0))) → c37(TOP(s(proper(z0))), PROPER(s(z0))) 226.18/72.87
TOP(mark(cons(z0, z1))) → c37(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.87
TOP(mark(add(z0, z1))) → c37(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.87
TOP(mark(0)) → c37(TOP(ok(0)))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, TOP, PROPER

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32, c32, c33, c33, c35, c35, c36, c36, c37, c37

226.18/72.87

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

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

TOP(mark(0)) → c37(TOP(ok(0)))

We considered the (Usable) Rules:

proper(fib(z0)) → fib(proper(z0)) 226.18/72.87
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.87
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.87
proper(s(z0)) → s(proper(z0)) 226.18/72.87
proper(0) → ok(0) 226.18/72.87
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.87
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.87
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.87
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.87
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.87
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.87
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.87
s(mark(z0)) → mark(s(z0)) 226.18/72.87
s(ok(z0)) → ok(s(z0)) 226.18/72.87
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.87
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.87
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.87
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.87
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.87
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.87
fib(mark(z0)) → mark(fib(z0)) 226.18/72.87
fib(ok(z0)) → ok(fib(z0)) 226.18/72.87
active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.87
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.87
active(add(0, z0)) → mark(z0) 226.18/72.87
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.87
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.87
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.87
active(fib(z0)) → fib(active(z0)) 226.18/72.87
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.87
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.87
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.87
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.87
active(s(z0)) → s(active(z0)) 226.18/72.87
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.87
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.87
active(add(z0, z1)) → add(z0, active(z1))

And the Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.87
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.87
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.87
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.87
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.87
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.87
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.87
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.88
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.88
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.88
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.88
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.88
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.88
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
TOP(mark(fib(z0))) → c37(TOP(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
TOP(mark(sel(z0, z1))) → c37(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
TOP(mark(fib1(z0, z1))) → c37(TOP(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
TOP(mark(s(z0))) → c37(TOP(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
TOP(mark(cons(z0, z1))) → c37(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
TOP(mark(add(z0, z1))) → c37(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
TOP(mark(0)) → c37(TOP(ok(0)))

The order we found is given by the following interpretation:
Polynomial interpretation : 226.18/72.88

POL(0) = 0 226.18/72.88
POL(ACTIVE(x₁)) = 0 226.18/72.88
POL(ADD(x₁, x₂)) = 0 226.18/72.88
POL(CONS(x₁, x₂)) = 0 226.18/72.88
POL(FIB(x₁)) = 0 226.18/72.88
POL(FIB1(x₁, x₂)) = 0 226.18/72.88
POL(PROPER(x₁)) = 0 226.18/72.88
POL(S(x₁)) = 0 226.18/72.88
POL(SEL(x₁, x₂)) = 0 226.18/72.88
POL(TOP(x₁)) = [2]x₁ 226.18/72.88
POL(active(x₁)) = x₁ 226.18/72.88
POL(add(x₁, x₂)) = [1] 226.18/72.88
POL(c(x₁)) = x₁ 226.18/72.88
POL(c1(x₁)) = x₁ 226.18/72.88
POL(c10(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c11(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c12(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c13(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c14(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c15(x₁)) = x₁ 226.18/72.88
POL(c16(x₁)) = x₁ 226.18/72.88
POL(c17(x₁)) = x₁ 226.18/72.88
POL(c18(x₁)) = x₁ 226.18/72.88
POL(c19(x₁)) = x₁ 226.18/72.88
POL(c20(x₁)) = x₁ 226.18/72.88
POL(c21(x₁)) = x₁ 226.18/72.88
POL(c22(x₁)) = x₁ 226.18/72.88
POL(c23(x₁)) = x₁ 226.18/72.88
POL(c24(x₁)) = x₁ 226.18/72.88
POL(c25(x₁)) = x₁ 226.18/72.88
POL(c26(x₁)) = x₁ 226.18/72.88
POL(c27(x₁)) = x₁ 226.18/72.88
POL(c28(x₁)) = x₁ 226.18/72.88
POL(c29(x₁)) = x₁ 226.18/72.88
POL(c3(x₁)) = x₁ 226.18/72.88
POL(c30(x₁)) = x₁ 226.18/72.88
POL(c30(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c31(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c31(x₁, x₂, x₃)) = x₁ + x₂ + x₃ 226.18/72.88
POL(c32(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c32(x₁, x₂, x₃)) = x₁ + x₂ + x₃ 226.18/72.88
POL(c33(x₁)) = x₁ 226.18/72.88
POL(c33(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c35(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c35(x₁, x₂, x₃)) = x₁ + x₂ + x₃ 226.18/72.88
POL(c36(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c36(x₁, x₂, x₃)) = x₁ + x₂ + x₃ 226.18/72.88
POL(c37(x₁)) = x₁ 226.18/72.88
POL(c37(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c38(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c5(x₁)) = x₁ 226.18/72.88
POL(c6(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c7(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c8(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(c9(x₁, x₂)) = x₁ + x₂ 226.18/72.88
POL(cons(x₁, x₂)) = [1] 226.18/72.88
POL(fib(x₁)) = [1] 226.18/72.88
POL(fib1(x₁, x₂)) = [1] 226.18/72.88
POL(mark(x₁)) = [1] 226.18/72.88
POL(ok(x₁)) = x₁ 226.18/72.88
POL(proper(x₁)) = 0 226.18/72.88
POL(s(x₁)) = [1] 226.18/72.88
POL(sel(x₁, x₂)) = [1]

226.18/72.88

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.88
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.88
active(add(0, z0)) → mark(z0) 226.18/72.88
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.88
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.88
active(fib(z0)) → fib(active(z0)) 226.18/72.88
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.88
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.88
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.88
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.88
active(s(z0)) → s(active(z0)) 226.18/72.88
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.88
fib(mark(z0)) → mark(fib(z0)) 226.18/72.88
fib(ok(z0)) → ok(fib(z0)) 226.18/72.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.88
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.88
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.88
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.88
s(mark(z0)) → mark(s(z0)) 226.18/72.88
s(ok(z0)) → ok(s(z0)) 226.18/72.88
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.88
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.88
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.88
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.88
proper(fib(z0)) → fib(proper(z0)) 226.18/72.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.88
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.88
proper(s(z0)) → s(proper(z0)) 226.18/72.88
proper(0) → ok(0) 226.18/72.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.88
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.88
top(mark(z0)) → top(proper(z0)) 226.18/72.88
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.88
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.88
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.88
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.88
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.88
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.88
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.88
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
TOP(mark(fib(z0))) → c37(TOP(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
TOP(mark(sel(z0, z1))) → c37(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
TOP(mark(fib1(z0, z1))) → c37(TOP(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
TOP(mark(s(z0))) → c37(TOP(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
TOP(mark(cons(z0, z1))) → c37(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
TOP(mark(add(z0, z1))) → c37(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
TOP(mark(0)) → c37(TOP(ok(0)))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.88
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.88
TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) 226.18/72.88
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.88
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.88
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.88
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.88
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
TOP(mark(fib(z0))) → c37(TOP(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
TOP(mark(sel(z0, z1))) → c37(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
TOP(mark(fib1(z0, z1))) → c37(TOP(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
TOP(mark(s(z0))) → c37(TOP(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
TOP(mark(cons(z0, z1))) → c37(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
TOP(mark(add(z0, z1))) → c37(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1)))

K tuples:

TOP(mark(0)) → c37(TOP(ok(0)))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, TOP, PROPER

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c38, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32, c32, c33, c33, c35, c35, c36, c36, c37, c37

226.18/72.88

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

Use narrowing to replace TOP(ok(z0)) → c38(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(fib(z0))) → c38(TOP(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(add(0, z0))) → c38(TOP(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
TOP(ok(add(s(z0), z1))) → c38(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
TOP(ok(sel(0, cons(z0, z1)))) → c38(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
TOP(ok(sel(s(z0), cons(z1, z2)))) → c38(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
TOP(ok(fib(z0))) → c38(TOP(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
TOP(ok(sel(z0, z1))) → c38(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
TOP(ok(sel(z0, z1))) → c38(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(s(z0))) → c38(TOP(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
TOP(ok(cons(z0, z1))) → c38(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
TOP(ok(add(z0, z1))) → c38(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
TOP(ok(add(z0, z1))) → c38(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1)))

226.18/72.88

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.88
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.88
active(add(0, z0)) → mark(z0) 226.18/72.88
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.88
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.88
active(fib(z0)) → fib(active(z0)) 226.18/72.88
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.88
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.88
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.88
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.88
active(s(z0)) → s(active(z0)) 226.18/72.88
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.88
fib(mark(z0)) → mark(fib(z0)) 226.18/72.88
fib(ok(z0)) → ok(fib(z0)) 226.18/72.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.88
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.88
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.88
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.88
s(mark(z0)) → mark(s(z0)) 226.18/72.88
s(ok(z0)) → ok(s(z0)) 226.18/72.88
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.88
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.88
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.88
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.88
proper(fib(z0)) → fib(proper(z0)) 226.18/72.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.88
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.88
proper(s(z0)) → s(proper(z0)) 226.18/72.88
proper(0) → ok(0) 226.18/72.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.88
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.88
top(mark(z0)) → top(proper(z0)) 226.18/72.88
top(ok(z0)) → top(active(z0))

Tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.88
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.88
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.88
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.88
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.88
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.88
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
TOP(mark(fib(z0))) → c37(TOP(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
TOP(mark(sel(z0, z1))) → c37(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
TOP(mark(fib1(z0, z1))) → c37(TOP(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
TOP(mark(s(z0))) → c37(TOP(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
TOP(mark(cons(z0, z1))) → c37(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
TOP(mark(add(z0, z1))) → c37(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
TOP(mark(0)) → c37(TOP(ok(0))) 226.18/72.88
TOP(ok(fib(z0))) → c38(TOP(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(add(0, z0))) → c38(TOP(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
TOP(ok(add(s(z0), z1))) → c38(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
TOP(ok(sel(0, cons(z0, z1)))) → c38(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
TOP(ok(sel(s(z0), cons(z1, z2)))) → c38(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
TOP(ok(fib(z0))) → c38(TOP(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
TOP(ok(sel(z0, z1))) → c38(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
TOP(ok(sel(z0, z1))) → c38(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(s(z0))) → c38(TOP(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
TOP(ok(cons(z0, z1))) → c38(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
TOP(ok(add(z0, z1))) → c38(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
TOP(ok(add(z0, z1))) → c38(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1)))

S tuples:

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.88
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.88
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.88
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.88
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.88
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.88
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
TOP(mark(fib(z0))) → c37(TOP(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
TOP(mark(sel(z0, z1))) → c37(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
TOP(mark(fib1(z0, z1))) → c37(TOP(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
TOP(mark(s(z0))) → c37(TOP(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
TOP(mark(cons(z0, z1))) → c37(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
TOP(mark(add(z0, z1))) → c37(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
TOP(ok(fib(z0))) → c38(TOP(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(add(0, z0))) → c38(TOP(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
TOP(ok(add(s(z0), z1))) → c38(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
TOP(ok(sel(0, cons(z0, z1)))) → c38(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
TOP(ok(sel(s(z0), cons(z1, z2)))) → c38(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
TOP(ok(fib(z0))) → c38(TOP(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
TOP(ok(sel(z0, z1))) → c38(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
TOP(ok(sel(z0, z1))) → c38(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(s(z0))) → c38(TOP(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
TOP(ok(cons(z0, z1))) → c38(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
TOP(ok(add(z0, z1))) → c38(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
TOP(ok(add(z0, z1))) → c38(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1)))

K tuples:

TOP(mark(0)) → c37(TOP(ok(0)))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

ACTIVE, FIB, SEL, FIB1, S, CONS, ADD, PROPER, TOP

Compound Symbols:

c5, c7, c8, c9, c10, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c, c1, c3, c6, c11, c12, c30, c30, c31, c31, c32, c32, c33, c33, c35, c35, c36, c36, c37, c37, c38

226.18/72.88

(43) CdtUnreachableProof (EQUIVALENT transformation)

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

ACTIVE(sel(s(z0), cons(z1, z2))) → c5(SEL(z0, z2)) 226.18/72.88
ACTIVE(sel(z0, z1)) → c7(SEL(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(sel(z0, z1)) → c8(SEL(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c9(FIB1(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c10(FIB1(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
ACTIVE(add(z0, z1)) → c13(ADD(active(z0), z1), ACTIVE(z0)) 226.18/72.88
ACTIVE(add(z0, z1)) → c14(ADD(z0, active(z1)), ACTIVE(z1)) 226.18/72.88
ACTIVE(fib(z0)) → c(SEL(z0, fib1(s(0), s(0)))) 226.18/72.88
ACTIVE(fib1(z0, z1)) → c1(ADD(z0, z1)) 226.18/72.88
ACTIVE(add(s(z0), z1)) → c3(ADD(z0, z1)) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(add(0, z0))) → c6(FIB(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(fib(add(s(z0), z1))) → c6(FIB(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(fib(sel(0, cons(z0, z1)))) → c6(FIB(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(fib(sel(s(z0), cons(z1, z2)))) → c6(FIB(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(fib(fib(z0))) → c6(FIB(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(sel(z0, z1))) → c6(FIB(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(fib1(z0, z1))) → c6(FIB(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(fib(s(z0))) → c6(FIB(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(fib(cons(z0, z1))) → c6(FIB(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(fib(add(z0, z1))) → c6(FIB(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(add(0, z0))) → c11(S(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(s(add(s(z0), z1))) → c11(S(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(s(sel(0, cons(z0, z1)))) → c11(S(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(s(sel(s(z0), cons(z1, z2)))) → c11(S(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(s(fib(z0))) → c11(S(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(sel(z0, z1))) → c11(S(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(fib1(z0, z1))) → c11(S(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(s(s(z0))) → c11(S(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(s(cons(z0, z1))) → c11(S(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(s(add(z0, z1))) → c11(S(add(z0, active(z1))), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(mark(sel(z0, fib1(s(0), s(0)))), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(mark(cons(z0, fib1(z1, add(z0, z1)))), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(add(0, z0), x1)) → c12(CONS(mark(z0), x1), ACTIVE(add(0, z0))) 226.18/72.88
ACTIVE(cons(add(s(z0), z1), x1)) → c12(CONS(mark(s(add(z0, z1))), x1), ACTIVE(add(s(z0), z1))) 226.18/72.88
ACTIVE(cons(sel(0, cons(z0, z1)), x1)) → c12(CONS(mark(z0), x1), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
ACTIVE(cons(sel(s(z0), cons(z1, z2)), x1)) → c12(CONS(mark(sel(z0, z2)), x1), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
ACTIVE(cons(fib(z0), x1)) → c12(CONS(fib(active(z0)), x1), ACTIVE(fib(z0))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(active(z0), z1), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(sel(z0, z1), x1)) → c12(CONS(sel(z0, active(z1)), x1), ACTIVE(sel(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(active(z0), z1), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(fib1(z0, z1), x1)) → c12(CONS(fib1(z0, active(z1)), x1), ACTIVE(fib1(z0, z1))) 226.18/72.88
ACTIVE(cons(s(z0), x1)) → c12(CONS(s(active(z0)), x1), ACTIVE(s(z0))) 226.18/72.88
ACTIVE(cons(cons(z0, z1), x1)) → c12(CONS(cons(active(z0), z1), x1), ACTIVE(cons(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(active(z0), z1), x1), ACTIVE(add(z0, z1))) 226.18/72.88
ACTIVE(cons(add(z0, z1), x1)) → c12(CONS(add(z0, active(z1)), x1), ACTIVE(add(z0, z1))) 226.18/72.88
PROPER(fib(fib(z0))) → c30(FIB(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(fib(sel(z0, z1))) → c30(FIB(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib(fib1(z0, z1))) → c30(FIB(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib(s(z0))) → c30(FIB(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(fib(cons(z0, z1))) → c30(FIB(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib(add(z0, z1))) → c30(FIB(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib(0)) → c30(FIB(ok(0))) 226.18/72.88
PROPER(sel(x0, fib(z0))) → c31(SEL(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(sel(x0, sel(z0, z1))) → c31(SEL(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(sel(x0, fib1(z0, z1))) → c31(SEL(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(sel(x0, s(z0))) → c31(SEL(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(sel(x0, cons(z0, z1))) → c31(SEL(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(sel(x0, add(z0, z1))) → c31(SEL(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(sel(fib(z0), x1)) → c31(SEL(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(sel(z0, z1), x1)) → c31(SEL(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(fib1(z0, z1), x1)) → c31(SEL(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(s(z0), x1)) → c31(SEL(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(sel(cons(z0, z1), x1)) → c31(SEL(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(add(z0, z1), x1)) → c31(SEL(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(sel(x0, 0)) → c31(SEL(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(sel(0, x1)) → c31(SEL(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, fib(z0))) → c32(FIB1(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(fib1(x0, sel(z0, z1))) → c32(FIB1(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(fib1(x0, fib1(z0, z1))) → c32(FIB1(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(fib1(x0, s(z0))) → c32(FIB1(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(fib1(x0, cons(z0, z1))) → c32(FIB1(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(fib1(x0, add(z0, z1))) → c32(FIB1(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(fib1(fib(z0), x1)) → c32(FIB1(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(sel(z0, z1), x1)) → c32(FIB1(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(fib1(z0, z1), x1)) → c32(FIB1(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(s(z0), x1)) → c32(FIB1(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(fib1(cons(z0, z1), x1)) → c32(FIB1(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(add(z0, z1), x1)) → c32(FIB1(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(fib1(x0, 0)) → c32(FIB1(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(fib1(0, x1)) → c32(FIB1(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(s(fib(z0))) → c33(S(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
PROPER(s(sel(z0, z1))) → c33(S(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(s(fib1(z0, z1))) → c33(S(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(s(s(z0))) → c33(S(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
PROPER(s(cons(z0, z1))) → c33(S(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(s(add(z0, z1))) → c33(S(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
PROPER(s(0)) → c33(S(ok(0))) 226.18/72.88
PROPER(cons(x0, fib(z0))) → c35(CONS(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(cons(x0, sel(z0, z1))) → c35(CONS(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(cons(x0, fib1(z0, z1))) → c35(CONS(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(cons(x0, s(z0))) → c35(CONS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(cons(x0, cons(z0, z1))) → c35(CONS(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(cons(x0, add(z0, z1))) → c35(CONS(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(cons(fib(z0), x1)) → c35(CONS(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(sel(z0, z1), x1)) → c35(CONS(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(fib1(z0, z1), x1)) → c35(CONS(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(s(z0), x1)) → c35(CONS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(cons(cons(z0, z1), x1)) → c35(CONS(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(add(z0, z1), x1)) → c35(CONS(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(cons(x0, 0)) → c35(CONS(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(cons(0, x1)) → c35(CONS(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, fib(z0))) → c36(ADD(proper(x0), fib(proper(z0))), PROPER(x0), PROPER(fib(z0))) 226.18/72.88
PROPER(add(x0, sel(z0, z1))) → c36(ADD(proper(x0), sel(proper(z0), proper(z1))), PROPER(x0), PROPER(sel(z0, z1))) 226.18/72.88
PROPER(add(x0, fib1(z0, z1))) → c36(ADD(proper(x0), fib1(proper(z0), proper(z1))), PROPER(x0), PROPER(fib1(z0, z1))) 226.18/72.88
PROPER(add(x0, s(z0))) → c36(ADD(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 226.18/72.88
PROPER(add(x0, cons(z0, z1))) → c36(ADD(proper(x0), cons(proper(z0), proper(z1))), PROPER(x0), PROPER(cons(z0, z1))) 226.18/72.88
PROPER(add(x0, add(z0, z1))) → c36(ADD(proper(x0), add(proper(z0), proper(z1))), PROPER(x0), PROPER(add(z0, z1))) 226.18/72.88
PROPER(add(fib(z0), x1)) → c36(ADD(fib(proper(z0)), proper(x1)), PROPER(fib(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(sel(z0, z1), x1)) → c36(ADD(sel(proper(z0), proper(z1)), proper(x1)), PROPER(sel(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(fib1(z0, z1), x1)) → c36(ADD(fib1(proper(z0), proper(z1)), proper(x1)), PROPER(fib1(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(s(z0), x1)) → c36(ADD(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 226.18/72.88
PROPER(add(cons(z0, z1), x1)) → c36(ADD(cons(proper(z0), proper(z1)), proper(x1)), PROPER(cons(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(add(z0, z1), x1)) → c36(ADD(add(proper(z0), proper(z1)), proper(x1)), PROPER(add(z0, z1)), PROPER(x1)) 226.18/72.88
PROPER(add(x0, 0)) → c36(ADD(proper(x0), ok(0)), PROPER(x0)) 226.18/72.88
PROPER(add(0, x1)) → c36(ADD(ok(0), proper(x1)), PROPER(x1)) 226.18/72.88
TOP(mark(fib(z0))) → c37(TOP(fib(proper(z0))), PROPER(fib(z0))) 226.18/72.88
TOP(mark(sel(z0, z1))) → c37(TOP(sel(proper(z0), proper(z1))), PROPER(sel(z0, z1))) 226.18/72.88
TOP(mark(fib1(z0, z1))) → c37(TOP(fib1(proper(z0), proper(z1))), PROPER(fib1(z0, z1))) 226.18/72.88
TOP(mark(s(z0))) → c37(TOP(s(proper(z0))), PROPER(s(z0))) 226.18/72.88
TOP(mark(cons(z0, z1))) → c37(TOP(cons(proper(z0), proper(z1))), PROPER(cons(z0, z1))) 226.18/72.88
TOP(mark(add(z0, z1))) → c37(TOP(add(proper(z0), proper(z1))), PROPER(add(z0, z1))) 226.18/72.88
TOP(ok(fib(z0))) → c38(TOP(mark(sel(z0, fib1(s(0), s(0))))), ACTIVE(fib(z0))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(mark(cons(z0, fib1(z1, add(z0, z1))))), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(add(0, z0))) → c38(TOP(mark(z0)), ACTIVE(add(0, z0))) 226.18/72.88
TOP(ok(add(s(z0), z1))) → c38(TOP(mark(s(add(z0, z1)))), ACTIVE(add(s(z0), z1))) 226.18/72.88
TOP(ok(sel(0, cons(z0, z1)))) → c38(TOP(mark(z0)), ACTIVE(sel(0, cons(z0, z1)))) 226.18/72.88
TOP(ok(sel(s(z0), cons(z1, z2)))) → c38(TOP(mark(sel(z0, z2))), ACTIVE(sel(s(z0), cons(z1, z2)))) 226.18/72.88
TOP(ok(fib(z0))) → c38(TOP(fib(active(z0))), ACTIVE(fib(z0))) 226.18/72.88
TOP(ok(sel(z0, z1))) → c38(TOP(sel(active(z0), z1)), ACTIVE(sel(z0, z1))) 226.18/72.88
TOP(ok(sel(z0, z1))) → c38(TOP(sel(z0, active(z1))), ACTIVE(sel(z0, z1))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(fib1(active(z0), z1)), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(fib1(z0, z1))) → c38(TOP(fib1(z0, active(z1))), ACTIVE(fib1(z0, z1))) 226.18/72.88
TOP(ok(s(z0))) → c38(TOP(s(active(z0))), ACTIVE(s(z0))) 226.18/72.88
TOP(ok(cons(z0, z1))) → c38(TOP(cons(active(z0), z1)), ACTIVE(cons(z0, z1))) 226.18/72.88
TOP(ok(add(z0, z1))) → c38(TOP(add(active(z0), z1)), ACTIVE(add(z0, z1))) 226.18/72.88
TOP(ok(add(z0, z1))) → c38(TOP(add(z0, active(z1))), ACTIVE(add(z0, z1)))

226.18/72.88

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.88
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.88
active(add(0, z0)) → mark(z0) 226.18/72.88
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.88
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.88
active(fib(z0)) → fib(active(z0)) 226.18/72.88
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.88
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.88
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.88
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.88
active(s(z0)) → s(active(z0)) 226.18/72.88
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.88
fib(mark(z0)) → mark(fib(z0)) 226.18/72.88
fib(ok(z0)) → ok(fib(z0)) 226.18/72.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.88
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.88
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.88
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.88
s(mark(z0)) → mark(s(z0)) 226.18/72.88
s(ok(z0)) → ok(s(z0)) 226.18/72.88
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.88
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.88
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.88
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.88
proper(fib(z0)) → fib(proper(z0)) 226.18/72.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.88
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.88
proper(s(z0)) → s(proper(z0)) 226.18/72.88
proper(0) → ok(0) 226.18/72.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.88
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.88
top(mark(z0)) → top(proper(z0)) 226.18/72.88
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.88
TOP(mark(0)) → c37(TOP(ok(0)))

S tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

K tuples:

TOP(mark(0)) → c37(TOP(ok(0)))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD, TOP

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c37

226.18/72.88

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

Removed 1 trailing tuple parts

226.18/72.88

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.88
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.88
active(add(0, z0)) → mark(z0) 226.18/72.88
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.88
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.88
active(fib(z0)) → fib(active(z0)) 226.18/72.88
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.88
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.88
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.88
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.88
active(s(z0)) → s(active(z0)) 226.18/72.88
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.88
fib(mark(z0)) → mark(fib(z0)) 226.18/72.88
fib(ok(z0)) → ok(fib(z0)) 226.18/72.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.88
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.88
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.88
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.88
s(mark(z0)) → mark(s(z0)) 226.18/72.88
s(ok(z0)) → ok(s(z0)) 226.18/72.88
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.88
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.88
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.88
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.88
proper(fib(z0)) → fib(proper(z0)) 226.18/72.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.88
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.88
proper(s(z0)) → s(proper(z0)) 226.18/72.88
proper(0) → ok(0) 226.18/72.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.88
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.88
top(mark(z0)) → top(proper(z0)) 226.18/72.88
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.88
TOP(mark(0)) → c37

S tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

K tuples:

TOP(mark(0)) → c37

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD, TOP

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c37

226.18/72.88

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

Removed 1 trailing nodes:

TOP(mark(0)) → c37

226.18/72.88

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.88
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.88
active(add(0, z0)) → mark(z0) 226.18/72.88
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.88
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.88
active(fib(z0)) → fib(active(z0)) 226.18/72.88
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.88
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.88
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.88
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.88
active(s(z0)) → s(active(z0)) 226.18/72.88
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.88
fib(mark(z0)) → mark(fib(z0)) 226.18/72.88
fib(ok(z0)) → ok(fib(z0)) 226.18/72.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.88
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.88
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.88
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.88
s(mark(z0)) → mark(s(z0)) 226.18/72.88
s(ok(z0)) → ok(s(z0)) 226.18/72.88
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.88
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.88
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.88
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.88
proper(fib(z0)) → fib(proper(z0)) 226.18/72.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.88
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.88
proper(s(z0)) → s(proper(z0)) 226.18/72.88
proper(0) → ok(0) 226.18/72.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.88
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.88
top(mark(z0)) → top(proper(z0)) 226.18/72.88
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

S tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

K tuples:none
Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29

226.18/72.88

(49) CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^3))) transformation)

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

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

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

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 226.18/72.88

POL(ADD(x₁, x₂)) = x₁² + x₁³ + x₁²·x₂ + x₁·x₂² 226.18/72.88
POL(CONS(x₁, x₂)) = 0 226.18/72.88
POL(FIB(x₁)) = x₁ + x₁² + x₁³ 226.18/72.88
POL(FIB1(x₁, x₂)) = 0 226.18/72.88
POL(S(x₁)) = x₁ + x₁² + x₁³ 226.18/72.88
POL(SEL(x₁, x₂)) = 0 226.18/72.88
POL(c15(x₁)) = x₁ 226.18/72.88
POL(c16(x₁)) = x₁ 226.18/72.88
POL(c17(x₁)) = x₁ 226.18/72.88
POL(c18(x₁)) = x₁ 226.18/72.88
POL(c19(x₁)) = x₁ 226.18/72.88
POL(c20(x₁)) = x₁ 226.18/72.88
POL(c21(x₁)) = x₁ 226.18/72.88
POL(c22(x₁)) = x₁ 226.18/72.88
POL(c23(x₁)) = x₁ 226.18/72.88
POL(c24(x₁)) = x₁ 226.18/72.88
POL(c25(x₁)) = x₁ 226.18/72.88
POL(c26(x₁)) = x₁ 226.18/72.88
POL(c27(x₁)) = x₁ 226.18/72.88
POL(c28(x₁)) = x₁ 226.18/72.88
POL(c29(x₁)) = x₁ 226.18/72.88
POL(mark(x₁)) = [1] + x₁ 226.18/72.88
POL(ok(x₁)) = [1] + x₁

226.18/72.88

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.88
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.88
active(add(0, z0)) → mark(z0) 226.18/72.88
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.88
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.88
active(fib(z0)) → fib(active(z0)) 226.18/72.88
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.88
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.88
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.88
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.88
active(s(z0)) → s(active(z0)) 226.18/72.88
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.88
fib(mark(z0)) → mark(fib(z0)) 226.18/72.88
fib(ok(z0)) → ok(fib(z0)) 226.18/72.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.88
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.88
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.88
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.88
s(mark(z0)) → mark(s(z0)) 226.18/72.88
s(ok(z0)) → ok(s(z0)) 226.18/72.88
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.88
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.88
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.88
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.88
proper(fib(z0)) → fib(proper(z0)) 226.18/72.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.88
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.88
proper(s(z0)) → s(proper(z0)) 226.18/72.88
proper(0) → ok(0) 226.18/72.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.88
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.88
top(mark(z0)) → top(proper(z0)) 226.18/72.88
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

S tuples:

SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1))

K tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29

226.18/72.88

(51) 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) → c25(CONS(z0, z1))

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

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 226.18/72.88

POL(ADD(x₁, x₂)) = [3]x₁ 226.18/72.88
POL(CONS(x₁, x₂)) = x₁ 226.18/72.88
POL(FIB(x₁)) = [3]x₁ 226.18/72.88
POL(FIB1(x₁, x₂)) = 0 226.18/72.88
POL(S(x₁)) = [5]x₁ 226.18/72.88
POL(SEL(x₁, x₂)) = 0 226.18/72.88
POL(c15(x₁)) = x₁ 226.18/72.88
POL(c16(x₁)) = x₁ 226.18/72.88
POL(c17(x₁)) = x₁ 226.18/72.88
POL(c18(x₁)) = x₁ 226.18/72.88
POL(c19(x₁)) = x₁ 226.18/72.88
POL(c20(x₁)) = x₁ 226.18/72.88
POL(c21(x₁)) = x₁ 226.18/72.88
POL(c22(x₁)) = x₁ 226.18/72.88
POL(c23(x₁)) = x₁ 226.18/72.88
POL(c24(x₁)) = x₁ 226.18/72.88
POL(c25(x₁)) = x₁ 226.18/72.88
POL(c26(x₁)) = x₁ 226.18/72.88
POL(c27(x₁)) = x₁ 226.18/72.88
POL(c28(x₁)) = x₁ 226.18/72.88
POL(c29(x₁)) = x₁ 226.18/72.88
POL(mark(x₁)) = [1] + x₁ 226.18/72.88
POL(ok(x₁)) = x₁

226.18/72.88

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.88
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.88
active(add(0, z0)) → mark(z0) 226.18/72.88
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.88
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.88
active(fib(z0)) → fib(active(z0)) 226.18/72.88
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.88
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.88
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.88
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.88
active(s(z0)) → s(active(z0)) 226.18/72.88
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.88
fib(mark(z0)) → mark(fib(z0)) 226.18/72.88
fib(ok(z0)) → ok(fib(z0)) 226.18/72.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.88
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.88
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.88
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.88
s(mark(z0)) → mark(s(z0)) 226.18/72.88
s(ok(z0)) → ok(s(z0)) 226.18/72.88
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.88
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.88
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.88
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.88
proper(fib(z0)) → fib(proper(z0)) 226.18/72.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.88
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.88
proper(s(z0)) → s(proper(z0)) 226.18/72.88
proper(0) → ok(0) 226.18/72.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.88
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.88
top(mark(z0)) → top(proper(z0)) 226.18/72.88
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

S tuples:

SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1))

K tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29

226.18/72.88

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

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

SEL(mark(z0), z1) → c17(SEL(z0, z1))

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

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 226.18/72.88

POL(ADD(x₁, x₂)) = [5]x₁ 226.18/72.88
POL(CONS(x₁, x₂)) = x₂ 226.18/72.88
POL(FIB(x₁)) = [3]x₁ 226.18/72.88
POL(FIB1(x₁, x₂)) = 0 226.18/72.88
POL(S(x₁)) = [3]x₁ 226.18/72.88
POL(SEL(x₁, x₂)) = [2]x₁ 226.18/72.88
POL(c15(x₁)) = x₁ 226.18/72.88
POL(c16(x₁)) = x₁ 226.18/72.88
POL(c17(x₁)) = x₁ 226.18/72.88
POL(c18(x₁)) = x₁ 226.18/72.88
POL(c19(x₁)) = x₁ 226.18/72.88
POL(c20(x₁)) = x₁ 226.18/72.88
POL(c21(x₁)) = x₁ 226.18/72.88
POL(c22(x₁)) = x₁ 226.18/72.88
POL(c23(x₁)) = x₁ 226.18/72.88
POL(c24(x₁)) = x₁ 226.18/72.88
POL(c25(x₁)) = x₁ 226.18/72.88
POL(c26(x₁)) = x₁ 226.18/72.88
POL(c27(x₁)) = x₁ 226.18/72.88
POL(c28(x₁)) = x₁ 226.18/72.88
POL(c29(x₁)) = x₁ 226.18/72.88
POL(mark(x₁)) = [1] + x₁ 226.18/72.88
POL(ok(x₁)) = x₁

226.18/72.88

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.88
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.88
active(add(0, z0)) → mark(z0) 226.18/72.88
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.88
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.88
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.88
active(fib(z0)) → fib(active(z0)) 226.18/72.88
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.88
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.88
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.88
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.88
active(s(z0)) → s(active(z0)) 226.18/72.88
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.88
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.88
fib(mark(z0)) → mark(fib(z0)) 226.18/72.88
fib(ok(z0)) → ok(fib(z0)) 226.18/72.88
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.88
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.88
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.88
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.88
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.88
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.88
s(mark(z0)) → mark(s(z0)) 226.18/72.88
s(ok(z0)) → ok(s(z0)) 226.18/72.88
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.88
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.88
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.88
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.88
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.88
proper(fib(z0)) → fib(proper(z0)) 226.18/72.88
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.88
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.88
proper(s(z0)) → s(proper(z0)) 226.18/72.88
proper(0) → ok(0) 226.18/72.88
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.88
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.88
top(mark(z0)) → top(proper(z0)) 226.18/72.88
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.88
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

S tuples:

SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.88
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.88
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.88
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.88
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.88
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.88
ADD(z0, mark(z1)) → c28(ADD(z0, z1))

K tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.88
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.88
S(mark(z0)) → c23(S(z0)) 226.18/72.88
S(ok(z0)) → c24(S(z0)) 226.18/72.88
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.88
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.88
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.88
SEL(mark(z0), z1) → c17(SEL(z0, z1))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29

226.18/72.89

(55) 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)) → c26(CONS(z0, z1))

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

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 226.18/72.89

POL(ADD(x₁, x₂)) = 0 226.18/72.89
POL(CONS(x₁, x₂)) = x₂² 226.18/72.89
POL(FIB(x₁)) = 0 226.18/72.89
POL(FIB1(x₁, x₂)) = 0 226.18/72.89
POL(S(x₁)) = 0 226.18/72.89
POL(SEL(x₁, x₂)) = 0 226.18/72.89
POL(c15(x₁)) = x₁ 226.18/72.89
POL(c16(x₁)) = x₁ 226.18/72.89
POL(c17(x₁)) = x₁ 226.18/72.89
POL(c18(x₁)) = x₁ 226.18/72.89
POL(c19(x₁)) = x₁ 226.18/72.89
POL(c20(x₁)) = x₁ 226.18/72.89
POL(c21(x₁)) = x₁ 226.18/72.89
POL(c22(x₁)) = x₁ 226.18/72.89
POL(c23(x₁)) = x₁ 226.18/72.89
POL(c24(x₁)) = x₁ 226.18/72.89
POL(c25(x₁)) = x₁ 226.18/72.89
POL(c26(x₁)) = x₁ 226.18/72.89
POL(c27(x₁)) = x₁ 226.18/72.89
POL(c28(x₁)) = x₁ 226.18/72.89
POL(c29(x₁)) = x₁ 226.18/72.89
POL(mark(x₁)) = 0 226.18/72.89
POL(ok(x₁)) = [1] + x₁

226.18/72.89

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.89
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.89
active(add(0, z0)) → mark(z0) 226.18/72.89
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.89
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.89
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.89
active(fib(z0)) → fib(active(z0)) 226.18/72.89
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.89
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.89
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.89
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.89
active(s(z0)) → s(active(z0)) 226.18/72.89
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.89
fib(mark(z0)) → mark(fib(z0)) 226.18/72.89
fib(ok(z0)) → ok(fib(z0)) 226.18/72.89
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.89
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.89
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.89
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.89
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.89
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.89
s(mark(z0)) → mark(s(z0)) 226.18/72.89
s(ok(z0)) → ok(s(z0)) 226.18/72.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.89
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.89
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.89
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.89
proper(fib(z0)) → fib(proper(z0)) 226.18/72.89
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.89
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.89
proper(s(z0)) → s(proper(z0)) 226.18/72.89
proper(0) → ok(0) 226.18/72.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.89
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.89
top(mark(z0)) → top(proper(z0)) 226.18/72.89
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

S tuples:

SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1))

K tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29

226.18/72.89

(57) 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.

FIB1(z0, mark(z1)) → c21(FIB1(z0, z1))

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

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 226.18/72.89

POL(ADD(x₁, x₂)) = x₁ + [3]x₁·x₂ + [3]x₁² 226.18/72.89
POL(CONS(x₁, x₂)) = x₁ + x₂ + [3]x₂² + [3]x₁·x₂ + [3]x₁² 226.18/72.89
POL(FIB(x₁)) = [3]x₁ + [3]x₁² 226.18/72.89
POL(FIB1(x₁, x₂)) = x₂ 226.18/72.89
POL(S(x₁)) = [3]x₁ + [3]x₁² 226.18/72.89
POL(SEL(x₁, x₂)) = 0 226.18/72.89
POL(c15(x₁)) = x₁ 226.18/72.89
POL(c16(x₁)) = x₁ 226.18/72.89
POL(c17(x₁)) = x₁ 226.18/72.89
POL(c18(x₁)) = x₁ 226.18/72.89
POL(c19(x₁)) = x₁ 226.18/72.89
POL(c20(x₁)) = x₁ 226.18/72.89
POL(c21(x₁)) = x₁ 226.18/72.89
POL(c22(x₁)) = x₁ 226.18/72.89
POL(c23(x₁)) = x₁ 226.18/72.89
POL(c24(x₁)) = x₁ 226.18/72.89
POL(c25(x₁)) = x₁ 226.18/72.89
POL(c26(x₁)) = x₁ 226.18/72.89
POL(c27(x₁)) = x₁ 226.18/72.89
POL(c28(x₁)) = x₁ 226.18/72.89
POL(c29(x₁)) = x₁ 226.18/72.89
POL(mark(x₁)) = [1] + x₁ 226.18/72.89
POL(ok(x₁)) = x₁

226.18/72.89

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.89
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.89
active(add(0, z0)) → mark(z0) 226.18/72.89
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.89
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.89
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.89
active(fib(z0)) → fib(active(z0)) 226.18/72.89
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.89
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.89
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.89
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.89
active(s(z0)) → s(active(z0)) 226.18/72.89
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.89
fib(mark(z0)) → mark(fib(z0)) 226.18/72.89
fib(ok(z0)) → ok(fib(z0)) 226.18/72.89
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.89
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.89
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.89
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.89
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.89
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.89
s(mark(z0)) → mark(s(z0)) 226.18/72.89
s(ok(z0)) → ok(s(z0)) 226.18/72.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.89
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.89
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.89
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.89
proper(fib(z0)) → fib(proper(z0)) 226.18/72.89
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.89
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.89
proper(s(z0)) → s(proper(z0)) 226.18/72.89
proper(0) → ok(0) 226.18/72.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.89
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.89
top(mark(z0)) → top(proper(z0)) 226.18/72.89
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

S tuples:

SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1))

K tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29

226.18/72.89

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

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

FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1))

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

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 226.18/72.89

POL(ADD(x₁, x₂)) = [3]x₁ 226.18/72.89
POL(CONS(x₁, x₂)) = [5]x₁ + [3]x₂ 226.18/72.89
POL(FIB(x₁)) = [5]x₁ 226.18/72.89
POL(FIB1(x₁, x₂)) = x₂ 226.18/72.89
POL(S(x₁)) = [3]x₁ 226.18/72.89
POL(SEL(x₁, x₂)) = 0 226.18/72.89
POL(c15(x₁)) = x₁ 226.18/72.89
POL(c16(x₁)) = x₁ 226.18/72.89
POL(c17(x₁)) = x₁ 226.18/72.89
POL(c18(x₁)) = x₁ 226.18/72.89
POL(c19(x₁)) = x₁ 226.18/72.89
POL(c20(x₁)) = x₁ 226.18/72.89
POL(c21(x₁)) = x₁ 226.18/72.89
POL(c22(x₁)) = x₁ 226.18/72.89
POL(c23(x₁)) = x₁ 226.18/72.89
POL(c24(x₁)) = x₁ 226.18/72.89
POL(c25(x₁)) = x₁ 226.18/72.89
POL(c26(x₁)) = x₁ 226.18/72.89
POL(c27(x₁)) = x₁ 226.18/72.89
POL(c28(x₁)) = x₁ 226.18/72.89
POL(c29(x₁)) = x₁ 226.18/72.89
POL(mark(x₁)) = x₁ 226.18/72.89
POL(ok(x₁)) = [1] + x₁

226.18/72.89

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.89
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.89
active(add(0, z0)) → mark(z0) 226.18/72.89
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.89
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.89
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.89
active(fib(z0)) → fib(active(z0)) 226.18/72.89
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.89
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.89
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.89
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.89
active(s(z0)) → s(active(z0)) 226.18/72.89
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.89
fib(mark(z0)) → mark(fib(z0)) 226.18/72.89
fib(ok(z0)) → ok(fib(z0)) 226.18/72.89
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.89
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.89
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.89
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.89
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.89
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.89
s(mark(z0)) → mark(s(z0)) 226.18/72.89
s(ok(z0)) → ok(s(z0)) 226.18/72.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.89
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.89
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.89
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.89
proper(fib(z0)) → fib(proper(z0)) 226.18/72.89
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.89
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.89
proper(s(z0)) → s(proper(z0)) 226.18/72.89
proper(0) → ok(0) 226.18/72.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.89
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.89
top(mark(z0)) → top(proper(z0)) 226.18/72.89
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

S tuples:

SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1))

K tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29

226.18/72.89

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

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

SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1))

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

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 226.18/72.89

POL(ADD(x₁, x₂)) = [3]x₁ + x₂ 226.18/72.89
POL(CONS(x₁, x₂)) = [3]x₁ + [5]x₂ 226.18/72.89
POL(FIB(x₁)) = [3]x₁ 226.18/72.89
POL(FIB1(x₁, x₂)) = [5]x₂ 226.18/72.89
POL(S(x₁)) = [3]x₁ 226.18/72.89
POL(SEL(x₁, x₂)) = x₁ + x₂ 226.18/72.89
POL(c15(x₁)) = x₁ 226.18/72.89
POL(c16(x₁)) = x₁ 226.18/72.89
POL(c17(x₁)) = x₁ 226.18/72.89
POL(c18(x₁)) = x₁ 226.18/72.89
POL(c19(x₁)) = x₁ 226.18/72.89
POL(c20(x₁)) = x₁ 226.18/72.89
POL(c21(x₁)) = x₁ 226.18/72.89
POL(c22(x₁)) = x₁ 226.18/72.89
POL(c23(x₁)) = x₁ 226.18/72.89
POL(c24(x₁)) = x₁ 226.18/72.89
POL(c25(x₁)) = x₁ 226.18/72.89
POL(c26(x₁)) = x₁ 226.18/72.89
POL(c27(x₁)) = x₁ 226.18/72.89
POL(c28(x₁)) = x₁ 226.18/72.89
POL(c29(x₁)) = x₁ 226.18/72.89
POL(mark(x₁)) = [1] + x₁ 226.18/72.89
POL(ok(x₁)) = x₁

226.18/72.89

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.89
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.89
active(add(0, z0)) → mark(z0) 226.18/72.89
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.89
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.89
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.89
active(fib(z0)) → fib(active(z0)) 226.18/72.89
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.89
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.89
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.89
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.89
active(s(z0)) → s(active(z0)) 226.18/72.89
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.89
fib(mark(z0)) → mark(fib(z0)) 226.18/72.89
fib(ok(z0)) → ok(fib(z0)) 226.18/72.89
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.89
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.89
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.89
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.89
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.89
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.89
s(mark(z0)) → mark(s(z0)) 226.18/72.89
s(ok(z0)) → ok(s(z0)) 226.18/72.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.89
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.89
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.89
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.89
proper(fib(z0)) → fib(proper(z0)) 226.18/72.89
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.89
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.89
proper(s(z0)) → s(proper(z0)) 226.18/72.89
proper(0) → ok(0) 226.18/72.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.89
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.89
top(mark(z0)) → top(proper(z0)) 226.18/72.89
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

S tuples:

SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1))

K tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29

226.18/72.89

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

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

SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1))

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

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 226.18/72.89

POL(ADD(x₁, x₂)) = [5]x₁ + [3]x₂ 226.18/72.89
POL(CONS(x₁, x₂)) = [3]x₁ + [5]x₂ 226.18/72.89
POL(FIB(x₁)) = [5]x₁ 226.18/72.89
POL(FIB1(x₁, x₂)) = [5]x₂ 226.18/72.89
POL(S(x₁)) = [3]x₁ 226.18/72.89
POL(SEL(x₁, x₂)) = x₁ 226.18/72.89
POL(c15(x₁)) = x₁ 226.18/72.89
POL(c16(x₁)) = x₁ 226.18/72.89
POL(c17(x₁)) = x₁ 226.18/72.89
POL(c18(x₁)) = x₁ 226.18/72.89
POL(c19(x₁)) = x₁ 226.18/72.89
POL(c20(x₁)) = x₁ 226.18/72.89
POL(c21(x₁)) = x₁ 226.18/72.89
POL(c22(x₁)) = x₁ 226.18/72.89
POL(c23(x₁)) = x₁ 226.18/72.89
POL(c24(x₁)) = x₁ 226.18/72.89
POL(c25(x₁)) = x₁ 226.18/72.89
POL(c26(x₁)) = x₁ 226.18/72.89
POL(c27(x₁)) = x₁ 226.18/72.89
POL(c28(x₁)) = x₁ 226.18/72.89
POL(c29(x₁)) = x₁ 226.18/72.89
POL(mark(x₁)) = [1] + x₁ 226.18/72.89
POL(ok(x₁)) = [2] + x₁

226.18/72.89

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.89
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.89
active(add(0, z0)) → mark(z0) 226.18/72.89
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.89
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.89
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.89
active(fib(z0)) → fib(active(z0)) 226.18/72.89
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.89
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.89
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.89
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.89
active(s(z0)) → s(active(z0)) 226.18/72.89
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.89
fib(mark(z0)) → mark(fib(z0)) 226.18/72.89
fib(ok(z0)) → ok(fib(z0)) 226.18/72.89
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.89
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.89
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.89
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.89
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.89
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.89
s(mark(z0)) → mark(s(z0)) 226.18/72.89
s(ok(z0)) → ok(s(z0)) 226.18/72.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.89
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.89
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.89
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.89
proper(fib(z0)) → fib(proper(z0)) 226.18/72.89
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.89
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.89
proper(s(z0)) → s(proper(z0)) 226.18/72.89
proper(0) → ok(0) 226.18/72.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.89
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.89
top(mark(z0)) → top(proper(z0)) 226.18/72.89
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

S tuples:

FIB1(mark(z0), z1) → c20(FIB1(z0, z1))

K tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29

226.18/72.89

(65) 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.

FIB1(mark(z0), z1) → c20(FIB1(z0, z1))

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

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

The order we found is given by the following interpretation:
Polynomial interpretation : 226.18/72.89

POL(ADD(x₁, x₂)) = [3]x₁ + [5]x₂ 226.18/72.89
POL(CONS(x₁, x₂)) = [5]x₁ + [5]x₂ 226.18/72.89
POL(FIB(x₁)) = [5]x₁ 226.18/72.89
POL(FIB1(x₁, x₂)) = [5]x₁ + [5]x₂ 226.18/72.89
POL(S(x₁)) = [5]x₁ 226.18/72.89
POL(SEL(x₁, x₂)) = [3]x₁ + [3]x₂ 226.18/72.89
POL(c15(x₁)) = x₁ 226.18/72.89
POL(c16(x₁)) = x₁ 226.18/72.89
POL(c17(x₁)) = x₁ 226.18/72.89
POL(c18(x₁)) = x₁ 226.18/72.89
POL(c19(x₁)) = x₁ 226.18/72.89
POL(c20(x₁)) = x₁ 226.18/72.89
POL(c21(x₁)) = x₁ 226.18/72.89
POL(c22(x₁)) = x₁ 226.18/72.89
POL(c23(x₁)) = x₁ 226.18/72.89
POL(c24(x₁)) = x₁ 226.18/72.89
POL(c25(x₁)) = x₁ 226.18/72.89
POL(c26(x₁)) = x₁ 226.18/72.89
POL(c27(x₁)) = x₁ 226.18/72.89
POL(c28(x₁)) = x₁ 226.18/72.89
POL(c29(x₁)) = x₁ 226.18/72.89
POL(mark(x₁)) = [1] + x₁ 226.18/72.89
POL(ok(x₁)) = x₁

226.18/72.89

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(fib(z0)) → mark(sel(z0, fib1(s(0), s(0)))) 226.18/72.89
active(fib1(z0, z1)) → mark(cons(z0, fib1(z1, add(z0, z1)))) 226.18/72.89
active(add(0, z0)) → mark(z0) 226.18/72.89
active(add(s(z0), z1)) → mark(s(add(z0, z1))) 226.18/72.89
active(sel(0, cons(z0, z1))) → mark(z0) 226.18/72.89
active(sel(s(z0), cons(z1, z2))) → mark(sel(z0, z2)) 226.18/72.89
active(fib(z0)) → fib(active(z0)) 226.18/72.89
active(sel(z0, z1)) → sel(active(z0), z1) 226.18/72.89
active(sel(z0, z1)) → sel(z0, active(z1)) 226.18/72.89
active(fib1(z0, z1)) → fib1(active(z0), z1) 226.18/72.89
active(fib1(z0, z1)) → fib1(z0, active(z1)) 226.18/72.89
active(s(z0)) → s(active(z0)) 226.18/72.89
active(cons(z0, z1)) → cons(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(active(z0), z1) 226.18/72.89
active(add(z0, z1)) → add(z0, active(z1)) 226.18/72.89
fib(mark(z0)) → mark(fib(z0)) 226.18/72.89
fib(ok(z0)) → ok(fib(z0)) 226.18/72.89
sel(mark(z0), z1) → mark(sel(z0, z1)) 226.18/72.89
sel(z0, mark(z1)) → mark(sel(z0, z1)) 226.18/72.89
sel(ok(z0), ok(z1)) → ok(sel(z0, z1)) 226.18/72.89
fib1(mark(z0), z1) → mark(fib1(z0, z1)) 226.18/72.89
fib1(z0, mark(z1)) → mark(fib1(z0, z1)) 226.18/72.89
fib1(ok(z0), ok(z1)) → ok(fib1(z0, z1)) 226.18/72.89
s(mark(z0)) → mark(s(z0)) 226.18/72.89
s(ok(z0)) → ok(s(z0)) 226.18/72.89
cons(mark(z0), z1) → mark(cons(z0, z1)) 226.18/72.89
cons(ok(z0), ok(z1)) → ok(cons(z0, z1)) 226.18/72.89
add(mark(z0), z1) → mark(add(z0, z1)) 226.18/72.89
add(z0, mark(z1)) → mark(add(z0, z1)) 226.18/72.89
add(ok(z0), ok(z1)) → ok(add(z0, z1)) 226.18/72.89
proper(fib(z0)) → fib(proper(z0)) 226.18/72.89
proper(sel(z0, z1)) → sel(proper(z0), proper(z1)) 226.18/72.89
proper(fib1(z0, z1)) → fib1(proper(z0), proper(z1)) 226.18/72.89
proper(s(z0)) → s(proper(z0)) 226.18/72.89
proper(0) → ok(0) 226.18/72.89
proper(cons(z0, z1)) → cons(proper(z0), proper(z1)) 226.18/72.89
proper(add(z0, z1)) → add(proper(z0), proper(z1)) 226.18/72.89
top(mark(z0)) → top(proper(z0)) 226.18/72.89
top(ok(z0)) → top(active(z0))

Tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1))

S tuples:none
K tuples:

FIB(mark(z0)) → c15(FIB(z0)) 226.18/72.89
FIB(ok(z0)) → c16(FIB(z0)) 226.18/72.89
S(mark(z0)) → c23(S(z0)) 226.18/72.89
S(ok(z0)) → c24(S(z0)) 226.18/72.89
ADD(mark(z0), z1) → c27(ADD(z0, z1)) 226.18/72.89
ADD(ok(z0), ok(z1)) → c29(ADD(z0, z1)) 226.18/72.89
CONS(mark(z0), z1) → c25(CONS(z0, z1)) 226.18/72.89
SEL(mark(z0), z1) → c17(SEL(z0, z1)) 226.18/72.89
CONS(ok(z0), ok(z1)) → c26(CONS(z0, z1)) 226.18/72.89
FIB1(z0, mark(z1)) → c21(FIB1(z0, z1)) 226.18/72.89
FIB1(ok(z0), ok(z1)) → c22(FIB1(z0, z1)) 226.18/72.89
SEL(z0, mark(z1)) → c18(SEL(z0, z1)) 226.18/72.89
ADD(z0, mark(z1)) → c28(ADD(z0, z1)) 226.18/72.89
SEL(ok(z0), ok(z1)) → c19(SEL(z0, z1)) 226.18/72.89
FIB1(mark(z0), z1) → c20(FIB1(z0, z1))

Defined Rule Symbols:

active, fib, sel, fib1, s, cons, add, proper, top

Defined Pair Symbols:

FIB, SEL, FIB1, S, CONS, ADD

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29

226.18/72.89

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

The set S is empty

226.18/72.89

(68) BOUNDS(O(1), O(1))

226.18/72.89