YES(O(1), O(n^1)) 384.63/117.67 YES(O(1), O(n^1)) 384.92/117.73 384.92/117.73 384.92/117.73 384.92/117.73 384.92/117.73 384.92/117.73 Runtime Complexity (innermost) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml.xml 384.92/117.73 384.92/117.73 384.92/117.73
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The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(n^1)).

0 CpxTRS
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↳1 CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
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↳2 CdtProblem
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↳3 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳4 CdtProblem
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↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
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↳6 CdtProblem
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↳7 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳8 CdtProblem
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↳9 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳10 CdtProblem
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↳11 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
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↳12 CdtProblem
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↳13 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳14 CdtProblem
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↳15 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳16 CdtProblem
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↳17 CdtGraphSplitRhsProof (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 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
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↳24 CdtProblem
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↳25 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳26 CdtProblem
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↳27 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳28 CdtProblem
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↳29 CdtGraphSplitRhsProof (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 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
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↳36 CdtProblem
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↳37 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳38 CdtProblem
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↳39 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳40 CdtProblem
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↳41 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
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↳42 CdtProblem
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↳43 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳44 CdtProblem
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↳45 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳46 CdtProblem
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↳47 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
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↳48 CdtProblem
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↳49 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳50 CdtProblem
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↳51 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳52 CdtProblem
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↳53 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳54 CdtProblem
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↳55 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳56 CdtProblem
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↳57 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳58 CdtProblem
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↳59 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳60 CdtProblem
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↳61 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳62 CdtProblem
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↳63 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳64 CdtProblem
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↳65 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳66 CdtProblem
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↳67 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳68 CdtProblem
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↳69 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳70 CdtProblem
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↳71 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳72 CdtProblem
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↳73 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳74 CdtProblem
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↳75 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳76 CdtProblem
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↳77 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳78 CdtProblem
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↳79 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳80 CdtProblem
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↳81 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳82 CdtProblem
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↳83 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳84 CdtProblem
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↳85 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳86 CdtProblem
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↳87 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳88 CdtProblem
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↳89 CdtNarrowingProof (BOTH BOUNDS(ID, ID))
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↳90 CdtProblem
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↳91 CdtUnreachableProof (⇔)
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↳92 CdtProblem
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↳93 CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
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↳94 CdtProblem
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↳95 CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
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↳96 CdtProblem
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↳97 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳98 CdtProblem
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↳99 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳100 CdtProblem
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↳101 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳102 CdtProblem
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↳103 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳104 CdtProblem
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↳105 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳106 CdtProblem
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↳107 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳108 CdtProblem
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↳109 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳110 CdtProblem
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↳111 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳112 CdtProblem
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↳113 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳114 CdtProblem
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↳115 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))))
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↳116 CdtProblem
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↳117 SIsEmptyProof (BOTH BOUNDS(ID, ID))
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↳118 BOUNDS(O(1), O(1))
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(0) Obligation:

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

active(U11(tt, V2)) → mark(U12(isNat(V2))) 384.92/117.73
active(U12(tt)) → mark(tt) 384.92/117.73
active(U21(tt)) → mark(tt) 384.92/117.73
active(U31(tt, N)) → mark(N) 384.92/117.73
active(U41(tt, M, N)) → mark(U42(isNat(N), M, N)) 384.92/117.73
active(U42(tt, M, N)) → mark(s(plus(N, M))) 384.92/117.73
active(isNat(0)) → mark(tt) 384.92/117.73
active(isNat(plus(V1, V2))) → mark(U11(isNat(V1), V2)) 384.92/117.73
active(isNat(s(V1))) → mark(U21(isNat(V1))) 384.92/117.73
active(plus(N, 0)) → mark(U31(isNat(N), N)) 384.92/117.73
active(plus(N, s(M))) → mark(U41(isNat(M), M, N)) 384.92/117.73
active(U11(X1, X2)) → U11(active(X1), X2) 384.92/117.73
active(U12(X)) → U12(active(X)) 384.92/117.76
active(U21(X)) → U21(active(X)) 384.92/117.76
active(U31(X1, X2)) → U31(active(X1), X2) 384.92/117.76
active(U41(X1, X2, X3)) → U41(active(X1), X2, X3) 384.92/117.76
active(U42(X1, X2, X3)) → U42(active(X1), X2, X3) 384.92/117.76
active(s(X)) → s(active(X)) 384.92/117.76
active(plus(X1, X2)) → plus(active(X1), X2) 384.92/117.76
active(plus(X1, X2)) → plus(X1, active(X2)) 384.92/117.76
U11(mark(X1), X2) → mark(U11(X1, X2)) 384.92/117.76
U12(mark(X)) → mark(U12(X)) 384.92/117.76
U21(mark(X)) → mark(U21(X)) 384.92/117.76
U31(mark(X1), X2) → mark(U31(X1, X2)) 384.92/117.76
U41(mark(X1), X2, X3) → mark(U41(X1, X2, X3)) 384.92/117.76
U42(mark(X1), X2, X3) → mark(U42(X1, X2, X3)) 384.92/117.76
s(mark(X)) → mark(s(X)) 384.92/117.76
plus(mark(X1), X2) → mark(plus(X1, X2)) 384.92/117.76
plus(X1, mark(X2)) → mark(plus(X1, X2)) 384.92/117.76
proper(U11(X1, X2)) → U11(proper(X1), proper(X2)) 384.92/117.76
proper(tt) → ok(tt) 384.92/117.76
proper(U12(X)) → U12(proper(X)) 384.92/117.76
proper(isNat(X)) → isNat(proper(X)) 384.92/117.76
proper(U21(X)) → U21(proper(X)) 384.92/117.76
proper(U31(X1, X2)) → U31(proper(X1), proper(X2)) 384.92/117.76
proper(U41(X1, X2, X3)) → U41(proper(X1), proper(X2), proper(X3)) 384.92/117.76
proper(U42(X1, X2, X3)) → U42(proper(X1), proper(X2), proper(X3)) 384.92/117.76
proper(s(X)) → s(proper(X)) 384.92/117.76
proper(plus(X1, X2)) → plus(proper(X1), proper(X2)) 384.92/117.76
proper(0) → ok(0) 384.92/117.76
U11(ok(X1), ok(X2)) → ok(U11(X1, X2)) 384.92/117.76
U12(ok(X)) → ok(U12(X)) 384.92/117.76
isNat(ok(X)) → ok(isNat(X)) 384.92/117.76
U21(ok(X)) → ok(U21(X)) 384.92/117.76
U31(ok(X1), ok(X2)) → ok(U31(X1, X2)) 384.92/117.76
U41(ok(X1), ok(X2), ok(X3)) → ok(U41(X1, X2, X3)) 384.92/117.76
U42(ok(X1), ok(X2), ok(X3)) → ok(U42(X1, X2, X3)) 384.92/117.76
s(ok(X)) → ok(s(X)) 384.92/117.76
plus(ok(X1), ok(X2)) → ok(plus(X1, X2)) 384.92/117.76
top(mark(X)) → top(proper(X)) 384.92/117.76
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(U11(tt, z0)) → mark(U12(isNat(z0))) 384.92/117.76
active(U12(tt)) → mark(tt) 384.92/117.76
active(U21(tt)) → mark(tt) 384.92/117.76
active(U31(tt, z0)) → mark(z0) 384.92/117.76
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 384.92/117.76
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 384.92/117.76
active(isNat(0)) → mark(tt) 384.92/117.76
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 384.92/117.76
active(isNat(s(z0))) → mark(U21(isNat(z0))) 384.92/117.76
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 384.92/117.76
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 384.92/117.76
active(U11(z0, z1)) → U11(active(z0), z1) 384.92/117.76
active(U12(z0)) → U12(active(z0)) 384.92/117.76
active(U21(z0)) → U21(active(z0)) 384.92/117.76
active(U31(z0, z1)) → U31(active(z0), z1) 384.92/117.76
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 384.92/117.76
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 384.92/117.76
active(s(z0)) → s(active(z0)) 384.92/117.76
active(plus(z0, z1)) → plus(active(z0), z1) 384.92/117.76
active(plus(z0, z1)) → plus(z0, active(z1)) 384.92/117.76
U11(mark(z0), z1) → mark(U11(z0, z1)) 384.92/117.76
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 384.92/117.76
U12(mark(z0)) → mark(U12(z0)) 384.92/117.76
U12(ok(z0)) → ok(U12(z0)) 384.92/117.76
U21(mark(z0)) → mark(U21(z0)) 384.92/117.76
U21(ok(z0)) → ok(U21(z0)) 384.92/117.76
U31(mark(z0), z1) → mark(U31(z0, z1)) 384.92/117.76
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 384.92/117.76
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 384.92/117.76
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 384.92/117.76
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 384.92/117.76
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 384.92/117.76
s(mark(z0)) → mark(s(z0)) 384.92/117.76
s(ok(z0)) → ok(s(z0)) 384.92/117.76
plus(mark(z0), z1) → mark(plus(z0, z1)) 384.92/117.76
plus(z0, mark(z1)) → mark(plus(z0, z1)) 384.92/117.76
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 384.92/117.76
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 384.92/117.76
proper(tt) → ok(tt) 384.92/117.76
proper(U12(z0)) → U12(proper(z0)) 384.92/117.76
proper(isNat(z0)) → isNat(proper(z0)) 384.92/117.76
proper(U21(z0)) → U21(proper(z0)) 384.92/117.76
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 384.92/117.76
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 384.92/117.76
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 384.92/117.76
proper(s(z0)) → s(proper(z0)) 384.92/117.76
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 384.92/117.76
proper(0) → ok(0) 384.92/117.76
isNat(ok(z0)) → ok(isNat(z0)) 384.92/117.76
top(mark(z0)) → top(proper(z0)) 384.92/117.76
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0)) 384.92/117.76
ACTIVE(U41(tt, z0, z1)) → c4(U42'(isNat(z1), z0, z1), ISNAT(z1)) 384.92/117.76
ACTIVE(U42(tt, z0, z1)) → c5(S(plus(z1, z0)), PLUS(z1, z0)) 384.92/117.76
ACTIVE(isNat(plus(z0, z1))) → c7(U11'(isNat(z0), z1), ISNAT(z0)) 384.92/117.76
ACTIVE(isNat(s(z0))) → c8(U21'(isNat(z0)), ISNAT(z0)) 384.92/117.76
ACTIVE(plus(z0, 0)) → c9(U31'(isNat(z0), z0), ISNAT(z0)) 384.92/117.76
ACTIVE(plus(z0, s(z1))) → c10(U41'(isNat(z1), z1, z0), ISNAT(z1)) 384.92/117.76
ACTIVE(U11(z0, z1)) → c11(U11'(active(z0), z1), ACTIVE(z0)) 384.92/117.76
ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 384.92/117.76
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 384.92/117.76
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 384.92/117.76
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 384.92/117.76
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 384.92/117.76
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 384.92/117.76
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 384.92/117.76
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 384.92/117.76
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 384.92/117.76
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 384.92/117.76
U12'(mark(z0)) → c22(U12'(z0)) 384.92/117.76
U12'(ok(z0)) → c23(U12'(z0)) 384.92/117.76
U21'(mark(z0)) → c24(U21'(z0)) 384.92/117.76
U21'(ok(z0)) → c25(U21'(z0)) 384.92/117.76
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 384.92/117.76
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 384.92/117.76
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 384.92/117.76
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 384.92/117.76
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 384.92/117.76
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 384.92/117.76
S(mark(z0)) → c32(S(z0)) 384.92/117.76
S(ok(z0)) → c33(S(z0)) 384.92/117.76
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 384.92/117.76
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 384.92/117.76
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 384.92/117.76
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 384.92/117.76
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 384.92/117.76
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 384.92/117.76
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 384.92/117.76
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 384.92/117.76
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 384.92/117.76
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 384.92/117.76
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 384.92/117.76
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 384.92/117.76
ISNAT(ok(z0)) → c48(ISNAT(z0)) 384.92/117.76
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 384.92/117.76
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0))
S tuples:

ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0)) 384.92/117.76
ACTIVE(U41(tt, z0, z1)) → c4(U42'(isNat(z1), z0, z1), ISNAT(z1)) 384.92/117.76
ACTIVE(U42(tt, z0, z1)) → c5(S(plus(z1, z0)), PLUS(z1, z0)) 384.92/117.76
ACTIVE(isNat(plus(z0, z1))) → c7(U11'(isNat(z0), z1), ISNAT(z0)) 384.92/117.76
ACTIVE(isNat(s(z0))) → c8(U21'(isNat(z0)), ISNAT(z0)) 384.92/117.76
ACTIVE(plus(z0, 0)) → c9(U31'(isNat(z0), z0), ISNAT(z0)) 384.92/117.76
ACTIVE(plus(z0, s(z1))) → c10(U41'(isNat(z1), z1, z0), ISNAT(z1)) 384.92/117.76
ACTIVE(U11(z0, z1)) → c11(U11'(active(z0), z1), ACTIVE(z0)) 384.92/117.76
ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 384.92/117.76
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 384.92/117.76
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 384.92/117.76
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 384.92/117.76
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 384.92/117.76
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 384.92/117.76
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 384.92/117.76
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 384.92/117.76
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 384.92/117.76
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 384.92/117.76
U12'(mark(z0)) → c22(U12'(z0)) 384.92/117.76
U12'(ok(z0)) → c23(U12'(z0)) 384.92/117.76
U21'(mark(z0)) → c24(U21'(z0)) 384.92/117.76
U21'(ok(z0)) → c25(U21'(z0)) 384.92/117.76
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 384.92/117.76
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 384.92/117.76
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 384.92/117.76
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 384.92/117.76
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 384.92/117.76
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 384.92/117.76
S(mark(z0)) → c32(S(z0)) 384.92/117.76
S(ok(z0)) → c33(S(z0)) 384.92/117.76
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 384.92/117.76
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 384.92/117.76
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 384.92/117.76
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 384.92/117.76
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 384.92/117.76
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 384.92/117.76
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 384.92/117.76
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 384.92/117.76
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 384.92/117.76
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 384.92/117.76
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 384.92/117.76
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 384.92/117.76
ISNAT(ok(z0)) → c48(ISNAT(z0)) 384.92/117.76
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 384.92/117.76
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c, c4, 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, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50

384.92/117.76
384.92/117.76

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

Removed 2 trailing tuple parts
384.92/117.76
384.92/117.76

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 384.92/117.76
active(U12(tt)) → mark(tt) 384.92/117.76
active(U21(tt)) → mark(tt) 384.92/117.76
active(U31(tt, z0)) → mark(z0) 384.92/117.76
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 384.92/117.76
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 384.92/117.76
active(isNat(0)) → mark(tt) 384.92/117.76
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 384.92/117.76
active(isNat(s(z0))) → mark(U21(isNat(z0))) 384.92/117.76
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 384.92/117.77
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 384.92/117.77
active(U11(z0, z1)) → U11(active(z0), z1) 384.92/117.77
active(U12(z0)) → U12(active(z0)) 384.92/117.77
active(U21(z0)) → U21(active(z0)) 384.92/117.77
active(U31(z0, z1)) → U31(active(z0), z1) 384.92/117.77
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 384.92/117.77
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 384.92/117.77
active(s(z0)) → s(active(z0)) 384.92/117.77
active(plus(z0, z1)) → plus(active(z0), z1) 384.92/117.77
active(plus(z0, z1)) → plus(z0, active(z1)) 384.92/117.77
U11(mark(z0), z1) → mark(U11(z0, z1)) 384.92/117.77
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 384.92/117.77
U12(mark(z0)) → mark(U12(z0)) 384.92/117.77
U12(ok(z0)) → ok(U12(z0)) 384.92/117.77
U21(mark(z0)) → mark(U21(z0)) 384.92/117.77
U21(ok(z0)) → ok(U21(z0)) 384.92/117.77
U31(mark(z0), z1) → mark(U31(z0, z1)) 384.92/117.77
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 384.92/117.77
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 384.92/117.77
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 384.92/117.77
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 384.92/117.77
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 384.92/117.77
s(mark(z0)) → mark(s(z0)) 384.92/117.77
s(ok(z0)) → ok(s(z0)) 384.92/117.77
plus(mark(z0), z1) → mark(plus(z0, z1)) 384.92/117.77
plus(z0, mark(z1)) → mark(plus(z0, z1)) 384.92/117.77
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 384.92/117.77
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 384.92/117.77
proper(tt) → ok(tt) 384.92/117.77
proper(U12(z0)) → U12(proper(z0)) 384.92/117.77
proper(isNat(z0)) → isNat(proper(z0)) 384.92/117.77
proper(U21(z0)) → U21(proper(z0)) 384.92/117.77
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 384.92/117.77
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 384.92/117.77
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 384.92/117.77
proper(s(z0)) → s(proper(z0)) 384.92/117.77
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 384.92/117.77
proper(0) → ok(0) 384.92/117.77
isNat(ok(z0)) → ok(isNat(z0)) 384.92/117.77
top(mark(z0)) → top(proper(z0)) 384.92/117.77
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0)) 384.92/117.77
ACTIVE(U41(tt, z0, z1)) → c4(U42'(isNat(z1), z0, z1), ISNAT(z1)) 384.92/117.77
ACTIVE(U42(tt, z0, z1)) → c5(S(plus(z1, z0)), PLUS(z1, z0)) 384.92/117.77
ACTIVE(isNat(plus(z0, z1))) → c7(U11'(isNat(z0), z1), ISNAT(z0)) 384.92/117.77
ACTIVE(plus(z0, 0)) → c9(U31'(isNat(z0), z0), ISNAT(z0)) 384.92/117.77
ACTIVE(U11(z0, z1)) → c11(U11'(active(z0), z1), ACTIVE(z0)) 384.92/117.77
ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 384.92/117.77
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 384.92/117.77
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 384.92/117.77
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 384.92/117.77
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 384.92/117.77
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 384.92/117.77
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 384.92/117.77
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 384.92/117.77
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 384.92/117.77
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 384.92/117.77
U12'(mark(z0)) → c22(U12'(z0)) 384.92/117.77
U12'(ok(z0)) → c23(U12'(z0)) 384.92/117.77
U21'(mark(z0)) → c24(U21'(z0)) 384.92/117.77
U21'(ok(z0)) → c25(U21'(z0)) 384.92/117.77
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 384.92/117.77
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 384.92/117.77
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 384.92/117.77
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 384.92/117.77
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 384.92/117.77
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 384.92/117.77
S(mark(z0)) → c32(S(z0)) 384.92/117.77
S(ok(z0)) → c33(S(z0)) 384.92/117.77
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 384.92/117.77
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 384.92/117.77
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 384.92/117.77
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 384.92/117.77
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 384.92/117.77
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 384.92/117.77
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 384.92/117.77
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 384.92/117.77
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 384.92/117.77
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 384.92/117.77
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 384.92/117.77
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 384.92/117.77
ISNAT(ok(z0)) → c48(ISNAT(z0)) 384.92/117.77
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 384.92/117.77
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 384.92/117.77
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 384.92/117.77
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1))
S tuples:

ACTIVE(U11(tt, z0)) → c(U12'(isNat(z0)), ISNAT(z0)) 384.92/117.77
ACTIVE(U41(tt, z0, z1)) → c4(U42'(isNat(z1), z0, z1), ISNAT(z1)) 384.92/117.77
ACTIVE(U42(tt, z0, z1)) → c5(S(plus(z1, z0)), PLUS(z1, z0)) 384.92/117.77
ACTIVE(isNat(plus(z0, z1))) → c7(U11'(isNat(z0), z1), ISNAT(z0)) 384.92/117.77
ACTIVE(plus(z0, 0)) → c9(U31'(isNat(z0), z0), ISNAT(z0)) 384.92/117.77
ACTIVE(U11(z0, z1)) → c11(U11'(active(z0), z1), ACTIVE(z0)) 384.92/117.77
ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 384.92/117.77
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 384.92/117.77
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 384.92/117.77
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 384.92/117.77
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 384.92/117.77
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 384.92/117.77
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 384.92/117.77
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 384.92/117.77
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 384.92/117.77
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 384.92/117.77
U12'(mark(z0)) → c22(U12'(z0)) 384.92/117.77
U12'(ok(z0)) → c23(U12'(z0)) 384.92/117.77
U21'(mark(z0)) → c24(U21'(z0)) 384.92/117.77
U21'(ok(z0)) → c25(U21'(z0)) 384.92/117.77
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 384.92/117.77
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 384.92/117.77
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 384.92/117.77
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 384.92/117.77
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.25/117.82
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.25/117.82
S(mark(z0)) → c32(S(z0)) 385.25/117.82
S(ok(z0)) → c33(S(z0)) 385.25/117.82
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.25/117.82
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.25/117.82
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.25/117.82
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.82
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.25/117.82
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.25/117.82
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.25/117.82
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.82
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.25/117.82
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.25/117.82
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.25/117.82
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.82
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.25/117.83
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.25/117.83
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.25/117.83
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c, c4, c5, c7, c9, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10

385.25/117.83
385.25/117.83

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

Split RHS of tuples not part of any SCC
385.25/117.83
385.25/117.83

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 385.25/117.83
active(U12(tt)) → mark(tt) 385.25/117.83
active(U21(tt)) → mark(tt) 385.25/117.83
active(U31(tt, z0)) → mark(z0) 385.25/117.83
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 385.25/117.83
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 385.25/117.83
active(isNat(0)) → mark(tt) 385.25/117.83
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 385.25/117.83
active(isNat(s(z0))) → mark(U21(isNat(z0))) 385.25/117.83
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 385.25/117.83
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 385.25/117.83
active(U11(z0, z1)) → U11(active(z0), z1) 385.25/117.83
active(U12(z0)) → U12(active(z0)) 385.25/117.83
active(U21(z0)) → U21(active(z0)) 385.25/117.83
active(U31(z0, z1)) → U31(active(z0), z1) 385.25/117.83
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 385.25/117.83
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 385.25/117.83
active(s(z0)) → s(active(z0)) 385.25/117.83
active(plus(z0, z1)) → plus(active(z0), z1) 385.25/117.83
active(plus(z0, z1)) → plus(z0, active(z1)) 385.25/117.83
U11(mark(z0), z1) → mark(U11(z0, z1)) 385.25/117.83
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 385.25/117.83
U12(mark(z0)) → mark(U12(z0)) 385.25/117.83
U12(ok(z0)) → ok(U12(z0)) 385.25/117.83
U21(mark(z0)) → mark(U21(z0)) 385.25/117.83
U21(ok(z0)) → ok(U21(z0)) 385.25/117.83
U31(mark(z0), z1) → mark(U31(z0, z1)) 385.25/117.83
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 385.25/117.83
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 385.25/117.83
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 385.25/117.83
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 385.25/117.83
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 385.25/117.83
s(mark(z0)) → mark(s(z0)) 385.25/117.83
s(ok(z0)) → ok(s(z0)) 385.25/117.83
plus(mark(z0), z1) → mark(plus(z0, z1)) 385.25/117.83
plus(z0, mark(z1)) → mark(plus(z0, z1)) 385.25/117.83
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 385.25/117.83
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 385.25/117.83
proper(tt) → ok(tt) 385.25/117.83
proper(U12(z0)) → U12(proper(z0)) 385.25/117.83
proper(isNat(z0)) → isNat(proper(z0)) 385.25/117.83
proper(U21(z0)) → U21(proper(z0)) 385.25/117.83
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 385.25/117.83
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 385.25/117.83
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 385.25/117.83
proper(s(z0)) → s(proper(z0)) 385.25/117.83
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 385.25/117.83
proper(0) → ok(0) 385.25/117.83
isNat(ok(z0)) → ok(isNat(z0)) 385.25/117.83
top(mark(z0)) → top(proper(z0)) 385.25/117.83
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U11(z0, z1)) → c11(U11'(active(z0), z1), ACTIVE(z0)) 385.25/117.83
ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.25/117.83
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.25/117.83
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.25/117.83
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.25/117.83
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.25/117.83
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.25/117.83
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.25/117.83
U12'(mark(z0)) → c22(U12'(z0)) 385.25/117.83
U12'(ok(z0)) → c23(U12'(z0)) 385.25/117.83
U21'(mark(z0)) → c24(U21'(z0)) 385.25/117.83
U21'(ok(z0)) → c25(U21'(z0)) 385.25/117.83
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.25/117.83
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.25/117.83
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.25/117.83
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.25/117.83
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.25/117.83
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.25/117.83
S(mark(z0)) → c32(S(z0)) 385.25/117.83
S(ok(z0)) → c33(S(z0)) 385.25/117.83
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.25/117.83
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.25/117.83
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.25/117.83
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.25/117.83
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.25/117.83
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.25/117.83
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.25/117.83
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.25/117.83
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.25/117.83
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.25/117.83
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.25/117.83
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.25/117.83
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.25/117.83
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.25/117.83
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.25/117.83
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.25/117.83
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.25/117.83
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.25/117.83
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
S tuples:

ACTIVE(U11(z0, z1)) → c11(U11'(active(z0), z1), ACTIVE(z0)) 385.25/117.83
ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.25/117.83
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.25/117.83
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.25/117.83
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.25/117.83
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.25/117.83
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.25/117.83
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.25/117.83
U12'(mark(z0)) → c22(U12'(z0)) 385.25/117.83
U12'(ok(z0)) → c23(U12'(z0)) 385.25/117.83
U21'(mark(z0)) → c24(U21'(z0)) 385.25/117.83
U21'(ok(z0)) → c25(U21'(z0)) 385.25/117.83
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.25/117.83
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.25/117.83
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.25/117.83
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.25/117.83
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.25/117.83
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.25/117.83
S(mark(z0)) → c32(S(z0)) 385.25/117.83
S(ok(z0)) → c33(S(z0)) 385.25/117.83
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.25/117.83
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.25/117.83
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.25/117.83
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.25/117.83
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.25/117.83
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.25/117.83
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.25/117.83
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.25/117.83
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.25/117.83
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.25/117.83
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.25/117.83
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.25/117.83
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.25/117.83
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.25/117.83
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.25/117.83
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.25/117.83
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.25/117.83
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.25/117.83
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1

385.25/117.83
385.25/117.83

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

Use narrowing to replace ACTIVE(U11(z0, z1)) → c11(U11'(active(z0), z1), ACTIVE(z0)) by

ACTIVE(U11(U11(tt, z0), x1)) → c11(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0))) 385.25/117.83
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U12(tt))) 385.25/117.83
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.25/117.83
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.25/117.83
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.25/117.83
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.25/117.83
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1), ACTIVE(isNat(0))) 385.25/117.83
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c11(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1)))) 385.25/117.83
ACTIVE(U11(isNat(s(z0)), x1)) → c11(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0)))) 385.25/117.83
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.25/117.83
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.25/117.83
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.25/117.83
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.25/117.83
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.25/117.83
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.25/117.83
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.25/117.83
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.25/117.83
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.25/117.83
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.25/117.83
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
385.25/117.83
385.25/117.83

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 385.25/117.83
active(U12(tt)) → mark(tt) 385.25/117.83
active(U21(tt)) → mark(tt) 385.25/117.83
active(U31(tt, z0)) → mark(z0) 385.25/117.83
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 385.25/117.83
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 385.25/117.83
active(isNat(0)) → mark(tt) 385.25/117.83
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 385.25/117.83
active(isNat(s(z0))) → mark(U21(isNat(z0))) 385.25/117.83
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 385.25/117.83
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 385.25/117.83
active(U11(z0, z1)) → U11(active(z0), z1) 385.25/117.83
active(U12(z0)) → U12(active(z0)) 385.25/117.83
active(U21(z0)) → U21(active(z0)) 385.25/117.83
active(U31(z0, z1)) → U31(active(z0), z1) 385.25/117.83
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 385.25/117.83
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 385.25/117.83
active(s(z0)) → s(active(z0)) 385.25/117.83
active(plus(z0, z1)) → plus(active(z0), z1) 385.25/117.83
active(plus(z0, z1)) → plus(z0, active(z1)) 385.25/117.83
U11(mark(z0), z1) → mark(U11(z0, z1)) 385.25/117.83
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 385.25/117.83
U12(mark(z0)) → mark(U12(z0)) 385.25/117.83
U12(ok(z0)) → ok(U12(z0)) 385.25/117.83
U21(mark(z0)) → mark(U21(z0)) 385.25/117.83
U21(ok(z0)) → ok(U21(z0)) 385.25/117.83
U31(mark(z0), z1) → mark(U31(z0, z1)) 385.25/117.83
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 385.25/117.83
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 385.25/117.83
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 385.25/117.83
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 385.25/117.83
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 385.25/117.83
s(mark(z0)) → mark(s(z0)) 385.25/117.83
s(ok(z0)) → ok(s(z0)) 385.25/117.83
plus(mark(z0), z1) → mark(plus(z0, z1)) 385.25/117.83
plus(z0, mark(z1)) → mark(plus(z0, z1)) 385.25/117.83
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 385.25/117.83
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 385.25/117.83
proper(tt) → ok(tt) 385.25/117.83
proper(U12(z0)) → U12(proper(z0)) 385.25/117.83
proper(isNat(z0)) → isNat(proper(z0)) 385.25/117.83
proper(U21(z0)) → U21(proper(z0)) 385.25/117.83
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 385.25/117.83
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 385.25/117.83
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 385.25/117.83
proper(s(z0)) → s(proper(z0)) 385.25/117.83
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 385.25/117.83
proper(0) → ok(0) 385.25/117.83
isNat(ok(z0)) → ok(isNat(z0)) 385.25/117.83
top(mark(z0)) → top(proper(z0)) 385.25/117.83
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.25/117.83
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.25/117.83
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.25/117.83
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.25/117.83
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.25/117.83
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.25/117.83
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.25/117.83
U12'(mark(z0)) → c22(U12'(z0)) 385.25/117.83
U12'(ok(z0)) → c23(U12'(z0)) 385.25/117.83
U21'(mark(z0)) → c24(U21'(z0)) 385.25/117.83
U21'(ok(z0)) → c25(U21'(z0)) 385.25/117.83
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.25/117.83
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.25/117.83
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.25/117.83
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.25/117.83
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.25/117.83
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.25/117.83
S(mark(z0)) → c32(S(z0)) 385.25/117.83
S(ok(z0)) → c33(S(z0)) 385.25/117.83
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.25/117.83
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.25/117.83
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.25/117.83
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.25/117.83
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.25/117.83
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.25/117.83
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.25/117.83
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.25/117.83
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.25/117.83
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.25/117.83
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.25/117.83
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.25/117.83
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.25/117.83
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.25/117.83
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.25/117.83
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.25/117.83
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.25/117.83
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.25/117.83
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.25/117.83
ACTIVE(U11(U11(tt, z0), x1)) → c11(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0))) 385.25/117.83
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U12(tt))) 385.25/117.83
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.25/117.83
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.25/117.83
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.25/117.83
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.25/117.83
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1), ACTIVE(isNat(0))) 385.25/117.83
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c11(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1)))) 385.25/117.83
ACTIVE(U11(isNat(s(z0)), x1)) → c11(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0)))) 385.25/117.83
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.25/117.83
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.25/117.83
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.25/117.83
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.25/117.83
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.25/117.83
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.25/117.83
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.25/117.83
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.25/117.83
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.25/117.83
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.25/117.83
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
S tuples:

ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.25/117.83
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.25/117.83
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.25/117.83
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.25/117.83
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.25/117.83
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.25/117.83
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.25/117.83
U12'(mark(z0)) → c22(U12'(z0)) 385.25/117.83
U12'(ok(z0)) → c23(U12'(z0)) 385.25/117.83
U21'(mark(z0)) → c24(U21'(z0)) 385.25/117.83
U21'(ok(z0)) → c25(U21'(z0)) 385.25/117.83
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.25/117.83
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.25/117.83
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.25/117.83
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.25/117.83
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.25/117.83
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.25/117.83
S(mark(z0)) → c32(S(z0)) 385.25/117.83
S(ok(z0)) → c33(S(z0)) 385.25/117.83
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.25/117.83
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.25/117.83
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.25/117.83
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.25/117.83
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.25/117.83
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.25/117.83
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.25/117.83
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.25/117.83
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.25/117.83
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.25/117.83
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.25/117.83
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.25/117.83
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.25/117.83
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.25/117.83
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.25/117.83
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.25/117.83
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.25/117.83
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.25/117.83
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.25/117.83
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.91
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.91
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.91
ACTIVE(U11(U11(tt, z0), x1)) → c11(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0))) 385.64/117.91
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U12(tt))) 385.64/117.91
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.91
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.91
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.91
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.91
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1), ACTIVE(isNat(0))) 385.64/117.91
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c11(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1)))) 385.64/117.91
ACTIVE(U11(isNat(s(z0)), x1)) → c11(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0)))) 385.64/117.91
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.91
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.91
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.91
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.91
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.91
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.91
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.91
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.91
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.91
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.91
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11

385.64/117.91
385.64/117.91

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

Removed 1 trailing tuple parts
385.64/117.91
385.64/117.91

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 385.64/117.91
active(U12(tt)) → mark(tt) 385.64/117.91
active(U21(tt)) → mark(tt) 385.64/117.91
active(U31(tt, z0)) → mark(z0) 385.64/117.91
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 385.64/117.91
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 385.64/117.91
active(isNat(0)) → mark(tt) 385.64/117.91
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 385.64/117.91
active(isNat(s(z0))) → mark(U21(isNat(z0))) 385.64/117.91
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 385.64/117.91
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 385.64/117.91
active(U11(z0, z1)) → U11(active(z0), z1) 385.64/117.91
active(U12(z0)) → U12(active(z0)) 385.64/117.91
active(U21(z0)) → U21(active(z0)) 385.64/117.91
active(U31(z0, z1)) → U31(active(z0), z1) 385.64/117.91
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 385.64/117.91
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 385.64/117.91
active(s(z0)) → s(active(z0)) 385.64/117.91
active(plus(z0, z1)) → plus(active(z0), z1) 385.64/117.91
active(plus(z0, z1)) → plus(z0, active(z1)) 385.64/117.91
U11(mark(z0), z1) → mark(U11(z0, z1)) 385.64/117.91
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 385.64/117.91
U12(mark(z0)) → mark(U12(z0)) 385.64/117.91
U12(ok(z0)) → ok(U12(z0)) 385.64/117.91
U21(mark(z0)) → mark(U21(z0)) 385.64/117.91
U21(ok(z0)) → ok(U21(z0)) 385.64/117.91
U31(mark(z0), z1) → mark(U31(z0, z1)) 385.64/117.91
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 385.64/117.91
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 385.64/117.91
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 385.64/117.91
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 385.64/117.91
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 385.64/117.91
s(mark(z0)) → mark(s(z0)) 385.64/117.91
s(ok(z0)) → ok(s(z0)) 385.64/117.91
plus(mark(z0), z1) → mark(plus(z0, z1)) 385.64/117.91
plus(z0, mark(z1)) → mark(plus(z0, z1)) 385.64/117.91
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 385.64/117.91
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 385.64/117.91
proper(tt) → ok(tt) 385.64/117.91
proper(U12(z0)) → U12(proper(z0)) 385.64/117.91
proper(isNat(z0)) → isNat(proper(z0)) 385.64/117.91
proper(U21(z0)) → U21(proper(z0)) 385.64/117.91
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 385.64/117.91
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 385.64/117.91
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 385.64/117.91
proper(s(z0)) → s(proper(z0)) 385.64/117.91
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 385.64/117.91
proper(0) → ok(0) 385.64/117.91
isNat(ok(z0)) → ok(isNat(z0)) 385.64/117.91
top(mark(z0)) → top(proper(z0)) 385.64/117.91
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 385.64/117.91
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.64/117.91
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.91
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.91
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.91
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.91
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.91
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.91
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.91
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.91
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.91
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.91
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.91
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.91
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.91
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.91
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.91
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.91
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.91
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.91
S(mark(z0)) → c32(S(z0)) 385.64/117.91
S(ok(z0)) → c33(S(z0)) 385.64/117.91
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.91
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.91
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.91
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.91
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.91
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.91
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.91
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.91
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.91
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.91
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.91
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.91
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.91
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.91
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.91
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.91
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.91
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.91
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.91
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.91
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.91
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.91
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.91
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.91
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.91
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.91
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.91
ACTIVE(U11(U11(tt, z0), x1)) → c11(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0))) 385.64/117.91
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U12(tt))) 385.64/117.91
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.91
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.91
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.91
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.91
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c11(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1)))) 385.64/117.91
ACTIVE(U11(isNat(s(z0)), x1)) → c11(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0)))) 385.64/117.91
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.91
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.91
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.91
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.91
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.91
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.91
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.91
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.91
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.91
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.91
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.91
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1))
S tuples:

ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 385.64/117.91
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.64/117.91
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.91
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.91
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.91
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.91
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.91
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.91
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.91
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.91
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.91
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.91
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.91
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.91
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.91
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.91
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.91
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.91
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.91
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.91
S(mark(z0)) → c32(S(z0)) 385.64/117.91
S(ok(z0)) → c33(S(z0)) 385.64/117.91
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.91
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.91
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.91
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.91
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.91
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.91
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.91
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.91
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.91
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.91
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.91
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.91
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.92
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.92
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.92
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.92
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.92
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.92
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.92
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.92
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.92
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.92
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.92
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.92
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.92
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.92
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.92
ACTIVE(U11(U11(tt, z0), x1)) → c11(U11'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0))) 385.64/117.92
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U12(tt))) 385.64/117.92
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.92
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.92
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.92
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.92
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c11(U11'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1)))) 385.64/117.92
ACTIVE(U11(isNat(s(z0)), x1)) → c11(U11'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0)))) 385.64/117.92
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.92
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.92
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.92
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.92
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.92
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.92
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.92
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.92
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.92
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.92
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.92
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11

385.64/117.92
385.64/117.92

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

Split RHS of tuples not part of any SCC
385.64/117.92
385.64/117.92

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 385.64/117.92
active(U12(tt)) → mark(tt) 385.64/117.92
active(U21(tt)) → mark(tt) 385.64/117.92
active(U31(tt, z0)) → mark(z0) 385.64/117.92
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 385.64/117.92
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 385.64/117.92
active(isNat(0)) → mark(tt) 385.64/117.92
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 385.64/117.92
active(isNat(s(z0))) → mark(U21(isNat(z0))) 385.64/117.92
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 385.64/117.92
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 385.64/117.92
active(U11(z0, z1)) → U11(active(z0), z1) 385.64/117.92
active(U12(z0)) → U12(active(z0)) 385.64/117.92
active(U21(z0)) → U21(active(z0)) 385.64/117.92
active(U31(z0, z1)) → U31(active(z0), z1) 385.64/117.92
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 385.64/117.92
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 385.64/117.92
active(s(z0)) → s(active(z0)) 385.64/117.92
active(plus(z0, z1)) → plus(active(z0), z1) 385.64/117.92
active(plus(z0, z1)) → plus(z0, active(z1)) 385.64/117.92
U11(mark(z0), z1) → mark(U11(z0, z1)) 385.64/117.92
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 385.64/117.92
U12(mark(z0)) → mark(U12(z0)) 385.64/117.92
U12(ok(z0)) → ok(U12(z0)) 385.64/117.92
U21(mark(z0)) → mark(U21(z0)) 385.64/117.92
U21(ok(z0)) → ok(U21(z0)) 385.64/117.92
U31(mark(z0), z1) → mark(U31(z0, z1)) 385.64/117.92
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 385.64/117.92
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 385.64/117.92
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 385.64/117.92
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 385.64/117.92
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 385.64/117.92
s(mark(z0)) → mark(s(z0)) 385.64/117.92
s(ok(z0)) → ok(s(z0)) 385.64/117.92
plus(mark(z0), z1) → mark(plus(z0, z1)) 385.64/117.92
plus(z0, mark(z1)) → mark(plus(z0, z1)) 385.64/117.92
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 385.64/117.92
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 385.64/117.92
proper(tt) → ok(tt) 385.64/117.92
proper(U12(z0)) → U12(proper(z0)) 385.64/117.92
proper(isNat(z0)) → isNat(proper(z0)) 385.64/117.92
proper(U21(z0)) → U21(proper(z0)) 385.64/117.92
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 385.64/117.92
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 385.64/117.92
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 385.64/117.92
proper(s(z0)) → s(proper(z0)) 385.64/117.92
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 385.64/117.92
proper(0) → ok(0) 385.64/117.92
isNat(ok(z0)) → ok(isNat(z0)) 385.64/117.92
top(mark(z0)) → top(proper(z0)) 385.64/117.92
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 385.64/117.92
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.64/117.92
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.92
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.92
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.92
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.92
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.92
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.92
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.92
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.92
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.92
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.92
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.92
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.92
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.92
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.92
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.92
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.92
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.92
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.92
S(mark(z0)) → c32(S(z0)) 385.64/117.92
S(ok(z0)) → c33(S(z0)) 385.64/117.92
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.92
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.92
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.92
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.92
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.92
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.92
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.92
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.92
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.92
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.92
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.92
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.92
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.92
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.92
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.92
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.92
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.92
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.92
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.92
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.92
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.92
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.92
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.92
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.92
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.92
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.92
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.92
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U12(tt))) 385.64/117.92
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.92
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.92
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.92
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.92
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.92
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.92
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.92
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.92
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.92
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.92
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.92
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.92
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.92
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.92
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.92
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.92
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 385.64/117.92
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 385.64/117.92
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 385.64/117.92
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.92
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 385.64/117.92
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
S tuples:

ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) 385.64/117.92
ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.64/117.92
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.92
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.92
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.92
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.92
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.92
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.92
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.92
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.92
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.92
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.92
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.92
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.92
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.92
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.92
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.92
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.92
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.92
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.92
S(mark(z0)) → c32(S(z0)) 385.64/117.92
S(ok(z0)) → c33(S(z0)) 385.64/117.92
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.92
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.92
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.92
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.92
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.92
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.92
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.92
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.92
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.92
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.92
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.92
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.92
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.93
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.93
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.93
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.93
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.93
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.93
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.93
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.93
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.93
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.93
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.93
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.93
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.93
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.93
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.93
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U12(tt))) 385.64/117.93
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.93
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.93
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.93
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.93
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.93
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.93
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.93
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.93
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.93
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.93
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.93
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.93
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.93
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.93
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.93
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.93
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 385.64/117.93
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 385.64/117.93
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 385.64/117.93
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.93
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 385.64/117.93
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0))))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c

385.64/117.93
385.64/117.93

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

Use narrowing to replace ACTIVE(U12(z0)) → c12(U12'(active(z0)), ACTIVE(z0)) by

ACTIVE(U12(U11(tt, z0))) → c12(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 385.64/117.93
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt)), ACTIVE(U12(tt))) 385.64/117.93
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.93
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.93
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 385.64/117.93
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 385.64/117.93
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt)), ACTIVE(isNat(0))) 385.64/117.93
ACTIVE(U12(isNat(plus(z0, z1)))) → c12(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 385.64/117.93
ACTIVE(U12(isNat(s(z0)))) → c12(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 385.64/117.93
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 385.64/117.93
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 385.64/117.93
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 385.64/117.93
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 385.64/117.93
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 385.64/117.93
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 385.64/117.93
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 385.64/117.93
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 385.64/117.93
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 385.64/117.93
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 385.64/117.93
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
385.64/117.93
385.64/117.93

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 385.64/117.93
active(U12(tt)) → mark(tt) 385.64/117.93
active(U21(tt)) → mark(tt) 385.64/117.93
active(U31(tt, z0)) → mark(z0) 385.64/117.93
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 385.64/117.93
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 385.64/117.93
active(isNat(0)) → mark(tt) 385.64/117.93
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 385.64/117.93
active(isNat(s(z0))) → mark(U21(isNat(z0))) 385.64/117.93
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 385.64/117.93
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 385.64/117.93
active(U11(z0, z1)) → U11(active(z0), z1) 385.64/117.93
active(U12(z0)) → U12(active(z0)) 385.64/117.93
active(U21(z0)) → U21(active(z0)) 385.64/117.93
active(U31(z0, z1)) → U31(active(z0), z1) 385.64/117.93
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 385.64/117.93
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 385.64/117.93
active(s(z0)) → s(active(z0)) 385.64/117.93
active(plus(z0, z1)) → plus(active(z0), z1) 385.64/117.93
active(plus(z0, z1)) → plus(z0, active(z1)) 385.64/117.93
U11(mark(z0), z1) → mark(U11(z0, z1)) 385.64/117.93
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 385.64/117.93
U12(mark(z0)) → mark(U12(z0)) 385.64/117.93
U12(ok(z0)) → ok(U12(z0)) 385.64/117.93
U21(mark(z0)) → mark(U21(z0)) 385.64/117.93
U21(ok(z0)) → ok(U21(z0)) 385.64/117.93
U31(mark(z0), z1) → mark(U31(z0, z1)) 385.64/117.93
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 385.64/117.93
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 385.64/117.93
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 385.64/117.93
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 385.64/117.93
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 385.64/117.93
s(mark(z0)) → mark(s(z0)) 385.64/117.93
s(ok(z0)) → ok(s(z0)) 385.64/117.93
plus(mark(z0), z1) → mark(plus(z0, z1)) 385.64/117.93
plus(z0, mark(z1)) → mark(plus(z0, z1)) 385.64/117.93
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 385.64/117.93
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 385.64/117.93
proper(tt) → ok(tt) 385.64/117.93
proper(U12(z0)) → U12(proper(z0)) 385.64/117.93
proper(isNat(z0)) → isNat(proper(z0)) 385.64/117.93
proper(U21(z0)) → U21(proper(z0)) 385.64/117.93
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 385.64/117.93
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 385.64/117.93
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 385.64/117.93
proper(s(z0)) → s(proper(z0)) 385.64/117.93
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 385.64/117.93
proper(0) → ok(0) 385.64/117.93
isNat(ok(z0)) → ok(isNat(z0)) 385.64/117.93
top(mark(z0)) → top(proper(z0)) 385.64/117.93
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.64/117.93
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.93
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.93
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.93
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.93
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.93
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.93
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.93
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.93
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.93
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.93
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.93
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.93
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.93
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.93
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.93
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.93
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.93
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.93
S(mark(z0)) → c32(S(z0)) 385.64/117.93
S(ok(z0)) → c33(S(z0)) 385.64/117.93
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.93
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.93
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.93
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.93
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.93
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.93
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.93
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.93
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.93
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.93
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.93
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.93
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.93
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.93
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.93
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.93
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.93
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.93
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.93
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.93
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.93
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.93
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.93
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.93
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.93
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.93
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.93
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U12(tt))) 385.64/117.93
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.93
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.93
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.93
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.93
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.93
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.93
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.93
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 385.64/117.94
ACTIVE(U12(U11(tt, z0))) → c12(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt)), ACTIVE(U12(tt))) 385.64/117.94
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.94
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.94
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt)), ACTIVE(isNat(0))) 385.64/117.94
ACTIVE(U12(isNat(plus(z0, z1)))) → c12(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U12(isNat(s(z0)))) → c12(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 385.64/117.94
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 385.64/117.94
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 385.64/117.94
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 385.64/117.94
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
S tuples:

ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.94
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.94
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.94
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.94
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.94
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.94
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.94
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.94
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.94
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.94
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.94
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.94
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.94
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.94
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.94
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.94
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.94
S(mark(z0)) → c32(S(z0)) 385.64/117.94
S(ok(z0)) → c33(S(z0)) 385.64/117.94
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.94
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.94
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.94
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.94
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.94
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.94
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.94
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.94
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.94
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.94
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.94
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.94
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.94
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.94
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.94
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.94
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U12(tt))) 385.64/117.94
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.94
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.94
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.94
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.94
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.94
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.94
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.94
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 385.64/117.94
ACTIVE(U12(U11(tt, z0))) → c12(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt)), ACTIVE(U12(tt))) 385.64/117.94
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.94
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.94
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt)), ACTIVE(isNat(0))) 385.64/117.94
ACTIVE(U12(isNat(plus(z0, z1)))) → c12(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U12(isNat(s(z0)))) → c12(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 385.64/117.94
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 385.64/117.94
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 385.64/117.94
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 385.64/117.94
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12

385.64/117.94
385.64/117.94

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

Removed 3 trailing tuple parts
385.64/117.94
385.64/117.94

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 385.64/117.94
active(U12(tt)) → mark(tt) 385.64/117.94
active(U21(tt)) → mark(tt) 385.64/117.94
active(U31(tt, z0)) → mark(z0) 385.64/117.94
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 385.64/117.94
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 385.64/117.94
active(isNat(0)) → mark(tt) 385.64/117.94
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 385.64/117.94
active(isNat(s(z0))) → mark(U21(isNat(z0))) 385.64/117.94
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 385.64/117.94
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 385.64/117.94
active(U11(z0, z1)) → U11(active(z0), z1) 385.64/117.94
active(U12(z0)) → U12(active(z0)) 385.64/117.94
active(U21(z0)) → U21(active(z0)) 385.64/117.94
active(U31(z0, z1)) → U31(active(z0), z1) 385.64/117.94
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 385.64/117.94
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 385.64/117.94
active(s(z0)) → s(active(z0)) 385.64/117.94
active(plus(z0, z1)) → plus(active(z0), z1) 385.64/117.94
active(plus(z0, z1)) → plus(z0, active(z1)) 385.64/117.94
U11(mark(z0), z1) → mark(U11(z0, z1)) 385.64/117.94
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 385.64/117.94
U12(mark(z0)) → mark(U12(z0)) 385.64/117.94
U12(ok(z0)) → ok(U12(z0)) 385.64/117.94
U21(mark(z0)) → mark(U21(z0)) 385.64/117.94
U21(ok(z0)) → ok(U21(z0)) 385.64/117.94
U31(mark(z0), z1) → mark(U31(z0, z1)) 385.64/117.94
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 385.64/117.94
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 385.64/117.94
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 385.64/117.94
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 385.64/117.94
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 385.64/117.94
s(mark(z0)) → mark(s(z0)) 385.64/117.94
s(ok(z0)) → ok(s(z0)) 385.64/117.94
plus(mark(z0), z1) → mark(plus(z0, z1)) 385.64/117.94
plus(z0, mark(z1)) → mark(plus(z0, z1)) 385.64/117.94
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 385.64/117.94
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 385.64/117.94
proper(tt) → ok(tt) 385.64/117.94
proper(U12(z0)) → U12(proper(z0)) 385.64/117.94
proper(isNat(z0)) → isNat(proper(z0)) 385.64/117.94
proper(U21(z0)) → U21(proper(z0)) 385.64/117.94
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 385.64/117.94
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 385.64/117.94
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 385.64/117.94
proper(s(z0)) → s(proper(z0)) 385.64/117.94
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 385.64/117.94
proper(0) → ok(0) 385.64/117.94
isNat(ok(z0)) → ok(isNat(z0)) 385.64/117.94
top(mark(z0)) → top(proper(z0)) 385.64/117.94
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.94
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.94
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.94
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.94
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.94
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.94
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.94
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.94
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.94
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.94
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.94
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.94
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.94
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.94
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.94
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.94
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.94
S(mark(z0)) → c32(S(z0)) 385.64/117.94
S(ok(z0)) → c33(S(z0)) 385.64/117.94
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.94
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.94
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.94
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.94
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.94
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.94
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.94
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.94
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.94
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.94
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.94
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.94
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.94
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.94
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.94
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.94
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.94
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.94
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.94
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.94
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.94
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.94
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.94
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 385.64/117.94
ACTIVE(U12(U11(tt, z0))) → c12(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.94
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.94
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(isNat(plus(z0, z1)))) → c12(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U12(isNat(s(z0)))) → c12(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 385.64/117.94
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 385.64/117.94
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 385.64/117.94
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 385.64/117.94
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.94
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 385.64/117.94
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt)))
S tuples:

ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.94
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.94
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.94
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.94
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.94
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.94
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.94
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.94
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.94
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.94
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.94
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.94
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.94
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.94
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.94
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.94
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.94
S(mark(z0)) → c32(S(z0)) 385.64/117.94
S(ok(z0)) → c33(S(z0)) 385.64/117.94
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.94
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.94
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.94
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.94
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.94
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.94
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.94
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.94
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.94
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.94
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.94
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.94
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.94
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.94
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.94
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.94
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.94
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.94
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.94
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.94
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.94
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.94
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.94
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 385.64/117.94
ACTIVE(U12(U11(tt, z0))) → c12(U12'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.94
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.94
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(isNat(plus(z0, z1)))) → c12(U12'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U12(isNat(s(z0)))) → c12(U12'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 385.64/117.94
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 385.64/117.94
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 385.64/117.94
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 385.64/117.94
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.94
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 385.64/117.94
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12

385.64/117.94
385.64/117.94

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

Split RHS of tuples not part of any SCC
385.64/117.94
385.64/117.94

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 385.64/117.94
active(U12(tt)) → mark(tt) 385.64/117.94
active(U21(tt)) → mark(tt) 385.64/117.94
active(U31(tt, z0)) → mark(z0) 385.64/117.94
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 385.64/117.94
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 385.64/117.94
active(isNat(0)) → mark(tt) 385.64/117.94
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 385.64/117.94
active(isNat(s(z0))) → mark(U21(isNat(z0))) 385.64/117.94
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 385.64/117.94
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 385.64/117.94
active(U11(z0, z1)) → U11(active(z0), z1) 385.64/117.94
active(U12(z0)) → U12(active(z0)) 385.64/117.94
active(U21(z0)) → U21(active(z0)) 385.64/117.94
active(U31(z0, z1)) → U31(active(z0), z1) 385.64/117.94
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 385.64/117.94
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 385.64/117.94
active(s(z0)) → s(active(z0)) 385.64/117.94
active(plus(z0, z1)) → plus(active(z0), z1) 385.64/117.94
active(plus(z0, z1)) → plus(z0, active(z1)) 385.64/117.94
U11(mark(z0), z1) → mark(U11(z0, z1)) 385.64/117.94
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 385.64/117.94
U12(mark(z0)) → mark(U12(z0)) 385.64/117.94
U12(ok(z0)) → ok(U12(z0)) 385.64/117.94
U21(mark(z0)) → mark(U21(z0)) 385.64/117.94
U21(ok(z0)) → ok(U21(z0)) 385.64/117.94
U31(mark(z0), z1) → mark(U31(z0, z1)) 385.64/117.94
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 385.64/117.94
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 385.64/117.94
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 385.64/117.94
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 385.64/117.94
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 385.64/117.94
s(mark(z0)) → mark(s(z0)) 385.64/117.94
s(ok(z0)) → ok(s(z0)) 385.64/117.94
plus(mark(z0), z1) → mark(plus(z0, z1)) 385.64/117.94
plus(z0, mark(z1)) → mark(plus(z0, z1)) 385.64/117.94
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 385.64/117.94
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 385.64/117.94
proper(tt) → ok(tt) 385.64/117.94
proper(U12(z0)) → U12(proper(z0)) 385.64/117.94
proper(isNat(z0)) → isNat(proper(z0)) 385.64/117.94
proper(U21(z0)) → U21(proper(z0)) 385.64/117.94
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 385.64/117.94
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 385.64/117.94
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 385.64/117.94
proper(s(z0)) → s(proper(z0)) 385.64/117.94
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 385.64/117.94
proper(0) → ok(0) 385.64/117.94
isNat(ok(z0)) → ok(isNat(z0)) 385.64/117.94
top(mark(z0)) → top(proper(z0)) 385.64/117.94
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.94
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.94
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.94
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.94
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.94
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.94
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.94
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.94
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.94
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.94
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.94
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.94
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.94
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.94
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.94
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.94
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.94
S(mark(z0)) → c32(S(z0)) 385.64/117.94
S(ok(z0)) → c33(S(z0)) 385.64/117.94
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.94
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.94
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.94
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.94
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.94
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.94
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.94
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.94
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.94
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.94
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.94
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.94
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.94
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.94
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.94
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.94
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.94
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.94
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.94
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.94
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.94
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.94
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.94
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 385.64/117.94
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.94
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.94
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 385.64/117.94
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 385.64/117.94
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 385.64/117.94
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.94
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 385.64/117.94
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 385.64/117.94
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 385.64/117.94
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 385.64/117.94
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 385.64/117.94
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
S tuples:

ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.94
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.94
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.94
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.94
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.94
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.94
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.94
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.94
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.94
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.94
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.94
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.94
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.94
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.94
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.94
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.94
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.94
S(mark(z0)) → c32(S(z0)) 385.64/117.94
S(ok(z0)) → c33(S(z0)) 385.64/117.94
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.94
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.94
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.94
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.94
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.94
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.94
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.94
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.94
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.94
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.94
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.94
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.94
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.94
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.94
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.94
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.94
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.94
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.94
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.94
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.94
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.94
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.94
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.94
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.94
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.94
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.94
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.94
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 385.64/117.94
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 385.64/117.94
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 385.64/117.94
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.94
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.94
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 385.64/117.94
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 385.64/117.94
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 385.64/117.94
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 385.64/117.94
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 385.64/117.94
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 385.64/117.94
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 385.64/117.94
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 385.64/117.94
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 385.64/117.94
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.94
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 385.64/117.94
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 385.64/117.94
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 385.64/117.94
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 385.64/117.94
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 385.64/117.94
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.94
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 385.64/117.94
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0))))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2

385.64/117.94
385.64/117.94

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

Use narrowing to replace ACTIVE(U21(z0)) → c13(U21'(active(z0)), ACTIVE(z0)) by

ACTIVE(U21(U11(tt, z0))) → c13(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 385.64/117.97
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt)), ACTIVE(U12(tt))) 385.64/117.97
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.97
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.97
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 385.64/117.97
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 385.64/117.97
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt)), ACTIVE(isNat(0))) 385.64/117.97
ACTIVE(U21(isNat(plus(z0, z1)))) → c13(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 385.64/117.97
ACTIVE(U21(isNat(s(z0)))) → c13(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 385.64/117.97
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 385.64/117.97
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 385.64/117.97
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 385.64/117.97
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 385.64/117.97
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 385.64/117.97
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 385.64/117.97
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 385.64/117.97
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 385.64/117.97
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 385.64/117.97
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 385.64/117.97
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
385.64/117.97
385.64/117.97

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 385.64/117.97
active(U12(tt)) → mark(tt) 385.64/117.97
active(U21(tt)) → mark(tt) 385.64/117.97
active(U31(tt, z0)) → mark(z0) 385.64/117.97
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 385.64/117.97
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 385.64/117.97
active(isNat(0)) → mark(tt) 385.64/117.97
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 385.64/117.97
active(isNat(s(z0))) → mark(U21(isNat(z0))) 385.64/117.97
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 385.64/117.97
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 385.64/117.97
active(U11(z0, z1)) → U11(active(z0), z1) 385.64/117.97
active(U12(z0)) → U12(active(z0)) 385.64/117.97
active(U21(z0)) → U21(active(z0)) 385.64/117.97
active(U31(z0, z1)) → U31(active(z0), z1) 385.64/117.97
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 385.64/117.97
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 385.64/117.97
active(s(z0)) → s(active(z0)) 385.64/117.97
active(plus(z0, z1)) → plus(active(z0), z1) 385.64/117.97
active(plus(z0, z1)) → plus(z0, active(z1)) 385.64/117.97
U11(mark(z0), z1) → mark(U11(z0, z1)) 385.64/117.97
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 385.64/117.97
U12(mark(z0)) → mark(U12(z0)) 385.64/117.97
U12(ok(z0)) → ok(U12(z0)) 385.64/117.97
U21(mark(z0)) → mark(U21(z0)) 385.64/117.97
U21(ok(z0)) → ok(U21(z0)) 385.64/117.97
U31(mark(z0), z1) → mark(U31(z0, z1)) 385.64/117.97
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 385.64/117.97
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 385.64/117.97
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 385.64/117.97
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 385.64/117.97
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 385.64/117.97
s(mark(z0)) → mark(s(z0)) 385.64/117.97
s(ok(z0)) → ok(s(z0)) 385.64/117.97
plus(mark(z0), z1) → mark(plus(z0, z1)) 385.64/117.97
plus(z0, mark(z1)) → mark(plus(z0, z1)) 385.64/117.97
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 385.64/117.97
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 385.64/117.97
proper(tt) → ok(tt) 385.64/117.97
proper(U12(z0)) → U12(proper(z0)) 385.64/117.97
proper(isNat(z0)) → isNat(proper(z0)) 385.64/117.97
proper(U21(z0)) → U21(proper(z0)) 385.64/117.97
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 385.64/117.97
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 385.64/117.97
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 385.64/117.97
proper(s(z0)) → s(proper(z0)) 385.64/117.97
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 385.64/117.97
proper(0) → ok(0) 385.64/117.97
isNat(ok(z0)) → ok(isNat(z0)) 385.64/117.97
top(mark(z0)) → top(proper(z0)) 385.64/117.97
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.97
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.97
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.97
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.97
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.97
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.97
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.97
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.97
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.97
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.97
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.97
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.97
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.97
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.97
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.97
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.97
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.97
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.97
S(mark(z0)) → c32(S(z0)) 385.64/117.97
S(ok(z0)) → c33(S(z0)) 385.64/117.97
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.97
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.97
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.97
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.97
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.97
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.97
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.97
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.97
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.97
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.97
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.97
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.97
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.97
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.97
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.97
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.97
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.97
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.97
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.97
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.97
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.97
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.97
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.97
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.97
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.97
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.97
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.97
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.97
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.97
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.97
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.97
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.97
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.97
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.97
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.97
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.97
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.97
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.97
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.97
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.97
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.97
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.97
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.97
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 385.64/117.97
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 385.64/117.97
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 385.64/117.97
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.97
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 385.64/117.97
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 385.64/117.97
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.97
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.97
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 385.64/117.97
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 385.64/117.97
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 385.64/117.97
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 385.64/117.97
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 385.64/117.97
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 385.64/117.97
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 385.64/117.97
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 385.64/117.97
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 385.64/117.97
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 385.64/117.97
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 385.64/117.97
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 385.64/117.97
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 385.64/117.97
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.97
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 385.64/117.97
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 385.64/117.97
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 385.64/117.97
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 385.64/117.97
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 385.64/117.97
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.97
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 385.64/117.97
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 385.64/117.97
ACTIVE(U21(U11(tt, z0))) → c13(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 385.64/117.97
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt)), ACTIVE(U12(tt))) 385.64/117.97
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.97
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.97
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 385.64/117.97
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 385.64/117.97
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt)), ACTIVE(isNat(0))) 385.64/117.97
ACTIVE(U21(isNat(plus(z0, z1)))) → c13(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 385.64/117.97
ACTIVE(U21(isNat(s(z0)))) → c13(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 385.64/117.97
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 385.64/117.97
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 385.64/117.97
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 385.64/117.97
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 385.64/117.97
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 385.64/117.97
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 385.64/117.97
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 385.64/117.97
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 385.64/117.97
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 385.64/117.97
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 385.64/117.97
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
S tuples:

ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 385.64/117.97
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.97
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 385.64/117.97
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 385.64/117.97
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 385.64/117.97
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 385.64/117.97
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 385.64/117.97
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 385.64/117.97
U12'(mark(z0)) → c22(U12'(z0)) 385.64/117.97
U12'(ok(z0)) → c23(U12'(z0)) 385.64/117.97
U21'(mark(z0)) → c24(U21'(z0)) 385.64/117.97
U21'(ok(z0)) → c25(U21'(z0)) 385.64/117.97
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 385.64/117.97
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 385.64/117.97
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 385.64/117.97
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 385.64/117.97
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 385.64/117.97
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 385.64/117.97
S(mark(z0)) → c32(S(z0)) 385.64/117.97
S(ok(z0)) → c33(S(z0)) 385.64/117.97
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 385.64/117.97
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 385.64/117.97
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 385.64/117.97
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.97
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 385.64/117.97
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 385.64/117.97
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 385.64/117.97
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.97
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.97
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 385.64/117.97
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 385.64/117.97
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 385.64/117.97
ISNAT(ok(z0)) → c48(ISNAT(z0)) 385.64/117.97
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 385.64/117.97
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 385.64/117.97
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 385.64/117.97
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 385.64/117.97
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 385.64/117.97
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 385.64/117.97
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 385.64/117.97
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 385.64/117.97
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 385.64/117.97
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 385.64/117.97
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 385.64/117.97
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 385.64/117.97
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 385.64/117.97
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 385.64/117.97
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1), ACTIVE(U21(tt))) 385.64/117.97
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 385.64/117.97
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 385.64/117.97
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 385.64/117.97
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 385.64/117.97
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 385.64/117.97
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 385.64/117.97
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 385.64/117.97
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 385.64/117.97
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 385.64/117.97
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 385.64/117.97
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 385.64/117.97
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 385.64/117.97
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 385.64/117.97
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 385.64/117.97
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.97
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 385.64/117.97
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 385.64/117.97
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 385.64/117.97
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.97
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 385.64/117.97
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 385.64/117.97
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.97
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.97
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 385.64/117.97
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 385.64/117.97
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 385.64/117.97
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 385.64/117.97
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 385.64/117.97
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 385.64/117.97
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 385.64/117.97
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 385.64/117.97
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 385.64/117.97
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 385.64/117.97
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 385.64/117.97
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 385.64/117.97
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 385.64/117.97
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 385.64/117.97
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 385.64/117.97
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 385.64/117.97
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 385.64/117.97
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 385.64/117.97
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 385.64/117.97
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 385.64/117.97
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 385.64/117.97
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 385.64/117.97
ACTIVE(U21(U11(tt, z0))) → c13(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 385.64/117.97
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt)), ACTIVE(U12(tt))) 385.64/117.97
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt)), ACTIVE(U21(tt))) 385.64/117.97
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0)), ACTIVE(U31(tt, z0))) 385.64/117.97
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.01
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.01
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt)), ACTIVE(isNat(0))) 386.03/118.01
ACTIVE(U21(isNat(plus(z0, z1)))) → c13(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.01
ACTIVE(U21(isNat(s(z0)))) → c13(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 386.03/118.01
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.01
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.01
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.01
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.01
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.01
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.01
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.01
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.01
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.01
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13

386.03/118.01
386.03/118.01

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

Removed 5 trailing tuple parts
386.03/118.01
386.03/118.01

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 386.03/118.01
active(U12(tt)) → mark(tt) 386.03/118.01
active(U21(tt)) → mark(tt) 386.03/118.01
active(U31(tt, z0)) → mark(z0) 386.03/118.01
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 386.03/118.01
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 386.03/118.01
active(isNat(0)) → mark(tt) 386.03/118.01
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 386.03/118.01
active(isNat(s(z0))) → mark(U21(isNat(z0))) 386.03/118.01
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 386.03/118.01
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 386.03/118.01
active(U11(z0, z1)) → U11(active(z0), z1) 386.03/118.01
active(U12(z0)) → U12(active(z0)) 386.03/118.01
active(U21(z0)) → U21(active(z0)) 386.03/118.01
active(U31(z0, z1)) → U31(active(z0), z1) 386.03/118.01
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 386.03/118.01
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 386.03/118.01
active(s(z0)) → s(active(z0)) 386.03/118.01
active(plus(z0, z1)) → plus(active(z0), z1) 386.03/118.01
active(plus(z0, z1)) → plus(z0, active(z1)) 386.03/118.01
U11(mark(z0), z1) → mark(U11(z0, z1)) 386.03/118.01
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 386.03/118.01
U12(mark(z0)) → mark(U12(z0)) 386.03/118.01
U12(ok(z0)) → ok(U12(z0)) 386.03/118.01
U21(mark(z0)) → mark(U21(z0)) 386.03/118.01
U21(ok(z0)) → ok(U21(z0)) 386.03/118.01
U31(mark(z0), z1) → mark(U31(z0, z1)) 386.03/118.01
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 386.03/118.01
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 386.03/118.01
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 386.03/118.01
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 386.03/118.01
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 386.03/118.01
s(mark(z0)) → mark(s(z0)) 386.03/118.01
s(ok(z0)) → ok(s(z0)) 386.03/118.01
plus(mark(z0), z1) → mark(plus(z0, z1)) 386.03/118.01
plus(z0, mark(z1)) → mark(plus(z0, z1)) 386.03/118.01
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 386.03/118.01
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 386.03/118.01
proper(tt) → ok(tt) 386.03/118.01
proper(U12(z0)) → U12(proper(z0)) 386.03/118.01
proper(isNat(z0)) → isNat(proper(z0)) 386.03/118.01
proper(U21(z0)) → U21(proper(z0)) 386.03/118.01
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 386.03/118.01
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 386.03/118.01
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 386.03/118.01
proper(s(z0)) → s(proper(z0)) 386.03/118.01
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 386.03/118.01
proper(0) → ok(0) 386.03/118.01
isNat(ok(z0)) → ok(isNat(z0)) 386.03/118.01
top(mark(z0)) → top(proper(z0)) 386.03/118.01
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 386.03/118.01
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.01
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.01
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.01
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.01
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.01
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.01
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.01
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.01
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.01
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.01
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.01
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.01
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.01
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.01
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.01
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.01
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.01
S(mark(z0)) → c32(S(z0)) 386.03/118.01
S(ok(z0)) → c33(S(z0)) 386.03/118.01
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.01
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.01
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.01
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.01
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.01
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.01
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.01
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.01
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.01
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.01
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.01
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.01
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.01
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.01
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.01
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.01
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.01
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.01
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.01
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.01
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.01
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.01
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.01
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 386.03/118.01
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.01
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.01
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.01
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.01
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.01
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.01
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.01
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.01
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.01
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.01
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.01
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.01
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.01
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.01
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.01
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.01
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.01
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.01
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.01
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.01
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.01
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.01
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.01
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.01
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.01
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.01
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.01
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.01
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.01
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.01
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.01
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.01
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.01
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.01
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.01
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.01
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.01
ACTIVE(U21(U11(tt, z0))) → c13(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 386.03/118.01
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.01
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.01
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.01
ACTIVE(U21(isNat(plus(z0, z1)))) → c13(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.01
ACTIVE(U21(isNat(s(z0)))) → c13(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 386.03/118.01
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.01
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.01
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.01
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.01
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.01
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.01
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.01
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.01
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.01
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.01
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.01
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.01
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.01
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt)))
S tuples:

ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 386.03/118.01
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.01
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.01
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.01
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.01
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.01
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.01
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.01
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.01
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.01
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.01
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.01
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.01
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.01
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.01
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.01
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.01
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.01
S(mark(z0)) → c32(S(z0)) 386.03/118.01
S(ok(z0)) → c33(S(z0)) 386.03/118.01
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.01
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.01
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.01
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.01
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.01
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.01
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.01
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.01
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.01
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.01
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.01
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.01
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.01
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.01
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.01
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.01
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.01
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.01
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.01
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.01
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.01
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.01
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.01
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 386.03/118.01
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.01
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.01
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.01
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.01
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.01
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.01
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.01
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.01
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.01
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.01
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.01
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.01
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.01
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.01
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.01
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.01
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.01
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.01
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.01
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.01
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.01
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.01
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.01
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.01
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.01
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.01
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.01
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.01
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.01
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.01
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.01
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.01
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.01
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.01
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.01
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.01
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.01
ACTIVE(U21(U11(tt, z0))) → c13(U21'(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 386.03/118.01
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.01
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.01
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.01
ACTIVE(U21(isNat(plus(z0, z1)))) → c13(U21'(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.01
ACTIVE(U21(isNat(s(z0)))) → c13(U21'(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 386.03/118.01
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.01
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.01
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.01
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.01
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.01
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.01
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.01
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.01
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.01
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.01
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.01
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.01
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.01
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13

386.03/118.01
386.03/118.01

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

Split RHS of tuples not part of any SCC
386.03/118.01
386.03/118.01

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 386.03/118.01
active(U12(tt)) → mark(tt) 386.03/118.01
active(U21(tt)) → mark(tt) 386.03/118.01
active(U31(tt, z0)) → mark(z0) 386.03/118.01
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 386.03/118.01
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 386.03/118.01
active(isNat(0)) → mark(tt) 386.03/118.01
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 386.03/118.01
active(isNat(s(z0))) → mark(U21(isNat(z0))) 386.03/118.01
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 386.03/118.01
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 386.03/118.01
active(U11(z0, z1)) → U11(active(z0), z1) 386.03/118.01
active(U12(z0)) → U12(active(z0)) 386.03/118.01
active(U21(z0)) → U21(active(z0)) 386.03/118.01
active(U31(z0, z1)) → U31(active(z0), z1) 386.03/118.01
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 386.03/118.01
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 386.03/118.01
active(s(z0)) → s(active(z0)) 386.03/118.01
active(plus(z0, z1)) → plus(active(z0), z1) 386.03/118.01
active(plus(z0, z1)) → plus(z0, active(z1)) 386.03/118.01
U11(mark(z0), z1) → mark(U11(z0, z1)) 386.03/118.01
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 386.03/118.01
U12(mark(z0)) → mark(U12(z0)) 386.03/118.01
U12(ok(z0)) → ok(U12(z0)) 386.03/118.01
U21(mark(z0)) → mark(U21(z0)) 386.03/118.01
U21(ok(z0)) → ok(U21(z0)) 386.03/118.01
U31(mark(z0), z1) → mark(U31(z0, z1)) 386.03/118.01
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 386.03/118.01
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 386.03/118.01
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 386.03/118.01
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 386.03/118.01
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 386.03/118.01
s(mark(z0)) → mark(s(z0)) 386.03/118.01
s(ok(z0)) → ok(s(z0)) 386.03/118.01
plus(mark(z0), z1) → mark(plus(z0, z1)) 386.03/118.01
plus(z0, mark(z1)) → mark(plus(z0, z1)) 386.03/118.01
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 386.03/118.01
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 386.03/118.01
proper(tt) → ok(tt) 386.03/118.01
proper(U12(z0)) → U12(proper(z0)) 386.03/118.01
proper(isNat(z0)) → isNat(proper(z0)) 386.03/118.01
proper(U21(z0)) → U21(proper(z0)) 386.03/118.01
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 386.03/118.01
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 386.03/118.01
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 386.03/118.01
proper(s(z0)) → s(proper(z0)) 386.03/118.01
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 386.03/118.01
proper(0) → ok(0) 386.03/118.01
isNat(ok(z0)) → ok(isNat(z0)) 386.03/118.01
top(mark(z0)) → top(proper(z0)) 386.03/118.01
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 386.03/118.01
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.01
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.01
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.01
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.01
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.01
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.01
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.01
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.01
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.01
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.01
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.01
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.01
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.01
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.01
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.01
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.01
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.01
S(mark(z0)) → c32(S(z0)) 386.03/118.01
S(ok(z0)) → c33(S(z0)) 386.03/118.01
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.01
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.01
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.01
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.01
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.01
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.01
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.01
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.01
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.01
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.01
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.01
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.01
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.01
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.01
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.01
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.01
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.01
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.01
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.01
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.01
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.01
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.01
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.01
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.01
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 386.03/118.01
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.01
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.01
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.01
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.01
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.01
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.01
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.01
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.01
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.01
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.01
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.01
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.01
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.01
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.01
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.01
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.01
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.01
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.01
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.01
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.01
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.01
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.01
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.01
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.01
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.01
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.01
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.01
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.01
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.01
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.01
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.01
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.01
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.01
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.01
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.01
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.01
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.01
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.01
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.01
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.01
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.01
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.01
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.01
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.01
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.01
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.01
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.01
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.01
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.01
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.01
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.01
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.01
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.01
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.01
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.01
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 386.03/118.01
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 386.03/118.01
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 386.03/118.01
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 386.03/118.01
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.01
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 386.03/118.01
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
S tuples:

ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) 386.03/118.01
ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.01
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.01
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.01
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.01
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.01
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.01
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.01
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.01
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.01
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.01
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.01
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.01
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.01
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.01
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.01
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.01
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.01
S(mark(z0)) → c32(S(z0)) 386.03/118.01
S(ok(z0)) → c33(S(z0)) 386.03/118.01
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.01
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.02
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.02
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.02
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.02
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.02
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.02
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.02
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.02
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.02
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.02
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.02
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.02
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.02
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.02
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.02
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.02
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.02
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.02
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.02
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.03
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.03
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.03
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.03
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.03
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.03
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.03
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 386.03/118.03
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.03
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.03
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.03
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.03
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.03
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.03
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.03
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.03
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.03
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.03
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.03
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.03
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.03
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.03
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.03
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.03
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.03
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.03
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.03
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.03
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.03
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.03
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.03
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.03
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.03
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.03
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.03
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.03
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.03
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.03
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.03
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.03
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.03
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.03
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.03
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.03
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.03
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.03
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.03
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.03
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.03
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.03
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.03
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.03
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.03
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.03
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.03
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.03
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.03
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.03
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.03
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.03
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.03
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.03
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.03
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.03
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.03
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.03
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.03
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.03
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.03
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 386.03/118.03
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 386.03/118.03
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 386.03/118.03
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 386.03/118.03
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.03
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 386.03/118.03
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0))))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3

386.03/118.03
386.03/118.03

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

Use narrowing to replace ACTIVE(U31(z0, z1)) → c14(U31'(active(z0), z1), ACTIVE(z0)) by

ACTIVE(U31(U11(tt, z0), x1)) → c14(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0))) 386.03/118.03
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1), ACTIVE(U12(tt))) 386.03/118.03
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1), ACTIVE(U21(tt))) 386.03/118.03
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1), ACTIVE(U31(tt, z0))) 386.03/118.03
ACTIVE(U31(U41(tt, z0, z1), x1)) → c14(U31'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.03
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.03
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1), ACTIVE(isNat(0))) 386.03/118.03
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c14(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.03
ACTIVE(U31(isNat(s(z0)), x1)) → c14(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0)))) 386.03/118.03
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.03
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.03
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.03
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.03
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.03
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.03
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.03
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.03
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.03
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.03
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
386.03/118.03
386.03/118.03

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 386.03/118.03
active(U12(tt)) → mark(tt) 386.03/118.03
active(U21(tt)) → mark(tt) 386.03/118.03
active(U31(tt, z0)) → mark(z0) 386.03/118.03
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 386.03/118.03
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 386.03/118.03
active(isNat(0)) → mark(tt) 386.03/118.03
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 386.03/118.03
active(isNat(s(z0))) → mark(U21(isNat(z0))) 386.03/118.03
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 386.03/118.03
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 386.03/118.03
active(U11(z0, z1)) → U11(active(z0), z1) 386.03/118.03
active(U12(z0)) → U12(active(z0)) 386.03/118.03
active(U21(z0)) → U21(active(z0)) 386.03/118.03
active(U31(z0, z1)) → U31(active(z0), z1) 386.03/118.03
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 386.03/118.03
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 386.03/118.03
active(s(z0)) → s(active(z0)) 386.03/118.03
active(plus(z0, z1)) → plus(active(z0), z1) 386.03/118.03
active(plus(z0, z1)) → plus(z0, active(z1)) 386.03/118.03
U11(mark(z0), z1) → mark(U11(z0, z1)) 386.03/118.03
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 386.03/118.03
U12(mark(z0)) → mark(U12(z0)) 386.03/118.03
U12(ok(z0)) → ok(U12(z0)) 386.03/118.03
U21(mark(z0)) → mark(U21(z0)) 386.03/118.03
U21(ok(z0)) → ok(U21(z0)) 386.03/118.03
U31(mark(z0), z1) → mark(U31(z0, z1)) 386.03/118.03
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 386.03/118.04
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 386.03/118.04
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 386.03/118.04
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 386.03/118.04
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 386.03/118.04
s(mark(z0)) → mark(s(z0)) 386.03/118.04
s(ok(z0)) → ok(s(z0)) 386.03/118.04
plus(mark(z0), z1) → mark(plus(z0, z1)) 386.03/118.04
plus(z0, mark(z1)) → mark(plus(z0, z1)) 386.03/118.04
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 386.03/118.04
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 386.03/118.04
proper(tt) → ok(tt) 386.03/118.04
proper(U12(z0)) → U12(proper(z0)) 386.03/118.04
proper(isNat(z0)) → isNat(proper(z0)) 386.03/118.04
proper(U21(z0)) → U21(proper(z0)) 386.03/118.04
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 386.03/118.04
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 386.03/118.04
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 386.03/118.04
proper(s(z0)) → s(proper(z0)) 386.03/118.04
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 386.03/118.04
proper(0) → ok(0) 386.03/118.04
isNat(ok(z0)) → ok(isNat(z0)) 386.03/118.04
top(mark(z0)) → top(proper(z0)) 386.03/118.04
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.04
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.04
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.04
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.04
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.04
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.04
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.04
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.04
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.04
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.04
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.04
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.04
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.04
S(mark(z0)) → c32(S(z0)) 386.03/118.04
S(ok(z0)) → c33(S(z0)) 386.03/118.04
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.04
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.04
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.04
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.04
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.04
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 386.03/118.04
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.04
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.04
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U31(U11(tt, z0), x1)) → c14(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1), ACTIVE(U12(tt))) 386.03/118.04
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1), ACTIVE(U21(tt))) 386.03/118.04
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1), ACTIVE(U31(tt, z0))) 386.03/118.04
ACTIVE(U31(U41(tt, z0, z1), x1)) → c14(U31'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1), ACTIVE(isNat(0))) 386.03/118.04
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c14(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U31(isNat(s(z0)), x1)) → c14(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
S tuples:

ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.04
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.04
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.04
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.04
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.04
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.04
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.04
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.04
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.04
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.04
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.04
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.04
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.04
S(mark(z0)) → c32(S(z0)) 386.03/118.04
S(ok(z0)) → c33(S(z0)) 386.03/118.04
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.04
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.04
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.04
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.04
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.04
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1), ACTIVE(U31(tt, z0))) 386.03/118.04
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.04
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0)), ACTIVE(U31(tt, z0))) 386.03/118.04
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U31(U11(tt, z0), x1)) → c14(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1), ACTIVE(U12(tt))) 386.03/118.04
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1), ACTIVE(U21(tt))) 386.03/118.04
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1), ACTIVE(U31(tt, z0))) 386.03/118.04
ACTIVE(U31(U41(tt, z0, z1), x1)) → c14(U31'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1), ACTIVE(isNat(0))) 386.03/118.04
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c14(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U31(isNat(s(z0)), x1)) → c14(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14

386.03/118.04
386.03/118.04

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

Removed 7 trailing tuple parts
386.03/118.04
386.03/118.04

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 386.03/118.04
active(U12(tt)) → mark(tt) 386.03/118.04
active(U21(tt)) → mark(tt) 386.03/118.04
active(U31(tt, z0)) → mark(z0) 386.03/118.04
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 386.03/118.04
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 386.03/118.04
active(isNat(0)) → mark(tt) 386.03/118.04
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 386.03/118.04
active(isNat(s(z0))) → mark(U21(isNat(z0))) 386.03/118.04
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 386.03/118.04
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 386.03/118.04
active(U11(z0, z1)) → U11(active(z0), z1) 386.03/118.04
active(U12(z0)) → U12(active(z0)) 386.03/118.04
active(U21(z0)) → U21(active(z0)) 386.03/118.04
active(U31(z0, z1)) → U31(active(z0), z1) 386.03/118.04
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 386.03/118.04
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 386.03/118.04
active(s(z0)) → s(active(z0)) 386.03/118.04
active(plus(z0, z1)) → plus(active(z0), z1) 386.03/118.04
active(plus(z0, z1)) → plus(z0, active(z1)) 386.03/118.04
U11(mark(z0), z1) → mark(U11(z0, z1)) 386.03/118.04
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 386.03/118.04
U12(mark(z0)) → mark(U12(z0)) 386.03/118.04
U12(ok(z0)) → ok(U12(z0)) 386.03/118.04
U21(mark(z0)) → mark(U21(z0)) 386.03/118.04
U21(ok(z0)) → ok(U21(z0)) 386.03/118.04
U31(mark(z0), z1) → mark(U31(z0, z1)) 386.03/118.04
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 386.03/118.04
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 386.03/118.04
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 386.03/118.04
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 386.03/118.04
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 386.03/118.04
s(mark(z0)) → mark(s(z0)) 386.03/118.04
s(ok(z0)) → ok(s(z0)) 386.03/118.04
plus(mark(z0), z1) → mark(plus(z0, z1)) 386.03/118.04
plus(z0, mark(z1)) → mark(plus(z0, z1)) 386.03/118.04
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 386.03/118.04
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 386.03/118.04
proper(tt) → ok(tt) 386.03/118.04
proper(U12(z0)) → U12(proper(z0)) 386.03/118.04
proper(isNat(z0)) → isNat(proper(z0)) 386.03/118.04
proper(U21(z0)) → U21(proper(z0)) 386.03/118.04
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 386.03/118.04
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 386.03/118.04
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 386.03/118.04
proper(s(z0)) → s(proper(z0)) 386.03/118.04
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 386.03/118.04
proper(0) → ok(0) 386.03/118.04
isNat(ok(z0)) → ok(isNat(z0)) 386.03/118.04
top(mark(z0)) → top(proper(z0)) 386.03/118.04
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.04
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.04
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.04
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.04
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.04
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.04
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.04
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.04
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.04
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.04
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.04
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.04
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.04
S(mark(z0)) → c32(S(z0)) 386.03/118.04
S(ok(z0)) → c33(S(z0)) 386.03/118.04
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.04
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.04
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.04
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.04
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.04
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U31(U11(tt, z0), x1)) → c14(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U31(U41(tt, z0, z1), x1)) → c14(U31'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c14(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U31(isNat(s(z0)), x1)) → c14(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 386.03/118.04
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 386.03/118.04
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 386.03/118.04
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.04
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.04
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 386.03/118.04
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1))
S tuples:

ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.04
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.04
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.04
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.04
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.04
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.04
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.04
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.04
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.04
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.04
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.04
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.04
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.04
S(mark(z0)) → c32(S(z0)) 386.03/118.04
S(ok(z0)) → c33(S(z0)) 386.03/118.04
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.04
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.04
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.04
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.04
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.04
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U31(U11(tt, z0), x1)) → c14(U31'(mark(U12(isNat(z0))), x1), ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U31(U41(tt, z0, z1), x1)) → c14(U31'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c14(U31'(mark(U11(isNat(z0), z1)), x1), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U31(isNat(s(z0)), x1)) → c14(U31'(mark(U21(isNat(z0))), x1), ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 386.03/118.04
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 386.03/118.04
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 386.03/118.04
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.04
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.04
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 386.03/118.04
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14

386.03/118.04
386.03/118.04

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

Split RHS of tuples not part of any SCC
386.03/118.04
386.03/118.04

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 386.03/118.04
active(U12(tt)) → mark(tt) 386.03/118.04
active(U21(tt)) → mark(tt) 386.03/118.04
active(U31(tt, z0)) → mark(z0) 386.03/118.04
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 386.03/118.04
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 386.03/118.04
active(isNat(0)) → mark(tt) 386.03/118.04
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 386.03/118.04
active(isNat(s(z0))) → mark(U21(isNat(z0))) 386.03/118.04
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 386.03/118.04
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 386.03/118.04
active(U11(z0, z1)) → U11(active(z0), z1) 386.03/118.04
active(U12(z0)) → U12(active(z0)) 386.03/118.04
active(U21(z0)) → U21(active(z0)) 386.03/118.04
active(U31(z0, z1)) → U31(active(z0), z1) 386.03/118.04
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 386.03/118.04
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 386.03/118.04
active(s(z0)) → s(active(z0)) 386.03/118.04
active(plus(z0, z1)) → plus(active(z0), z1) 386.03/118.04
active(plus(z0, z1)) → plus(z0, active(z1)) 386.03/118.04
U11(mark(z0), z1) → mark(U11(z0, z1)) 386.03/118.04
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 386.03/118.04
U12(mark(z0)) → mark(U12(z0)) 386.03/118.04
U12(ok(z0)) → ok(U12(z0)) 386.03/118.04
U21(mark(z0)) → mark(U21(z0)) 386.03/118.04
U21(ok(z0)) → ok(U21(z0)) 386.03/118.04
U31(mark(z0), z1) → mark(U31(z0, z1)) 386.03/118.04
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 386.03/118.04
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 386.03/118.04
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 386.03/118.04
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 386.03/118.04
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 386.03/118.04
s(mark(z0)) → mark(s(z0)) 386.03/118.04
s(ok(z0)) → ok(s(z0)) 386.03/118.04
plus(mark(z0), z1) → mark(plus(z0, z1)) 386.03/118.04
plus(z0, mark(z1)) → mark(plus(z0, z1)) 386.03/118.04
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 386.03/118.04
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 386.03/118.04
proper(tt) → ok(tt) 386.03/118.04
proper(U12(z0)) → U12(proper(z0)) 386.03/118.04
proper(isNat(z0)) → isNat(proper(z0)) 386.03/118.04
proper(U21(z0)) → U21(proper(z0)) 386.03/118.04
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 386.03/118.04
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 386.03/118.04
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 386.03/118.04
proper(s(z0)) → s(proper(z0)) 386.03/118.04
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 386.03/118.04
proper(0) → ok(0) 386.03/118.04
isNat(ok(z0)) → ok(isNat(z0)) 386.03/118.04
top(mark(z0)) → top(proper(z0)) 386.03/118.04
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.04
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.04
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.04
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.04
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.04
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.04
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.04
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.04
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.04
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.04
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.04
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.04
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.04
S(mark(z0)) → c32(S(z0)) 386.03/118.04
S(ok(z0)) → c33(S(z0)) 386.03/118.04
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.04
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.04
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.04
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.04
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.04
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U31(U41(tt, z0, z1), x1)) → c14(U31'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 386.03/118.04
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 386.03/118.04
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 386.03/118.04
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.04
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.04
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 386.03/118.04
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.04
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.04
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
S tuples:

ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.04
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.04
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.04
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.04
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.04
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.04
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.04
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.04
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.04
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.04
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.04
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.04
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.04
S(mark(z0)) → c32(S(z0)) 386.03/118.04
S(ok(z0)) → c33(S(z0)) 386.03/118.04
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.04
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.04
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.04
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.04
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.04
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.04
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.04
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.04
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 386.03/118.04
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 386.03/118.04
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 386.03/118.04
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U31(U41(tt, z0, z1), x1)) → c14(U31'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 386.03/118.04
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 386.03/118.04
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 386.03/118.04
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.04
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.04
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 386.03/118.04
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.04
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.04
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 386.03/118.04
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0))))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4

386.03/118.04
386.03/118.04

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

Use narrowing to replace ACTIVE(U41(z0, z1, z2)) → c15(U41'(active(z0), z1, z2), ACTIVE(z0)) by

ACTIVE(U41(U11(tt, z0), x1, x2)) → c15(U41'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0))) 386.03/118.04
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2), ACTIVE(U12(tt))) 386.03/118.04
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2), ACTIVE(U21(tt))) 386.03/118.04
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2), ACTIVE(U31(tt, z0))) 386.03/118.04
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c15(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c15(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 386.03/118.04
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2), ACTIVE(isNat(0))) 386.03/118.04
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c15(U41'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.04
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c15(U41'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0)))) 386.03/118.04
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 386.03/118.04
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 386.03/118.04
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 386.03/118.04
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 386.03/118.04
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 386.03/118.04
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 386.03/118.04
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 386.03/118.04
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 386.03/118.04
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 386.03/118.04
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 386.03/118.04
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
386.03/118.04
386.03/118.04

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 386.03/118.04
active(U12(tt)) → mark(tt) 386.03/118.04
active(U21(tt)) → mark(tt) 386.03/118.04
active(U31(tt, z0)) → mark(z0) 386.03/118.04
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 386.03/118.04
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 386.03/118.04
active(isNat(0)) → mark(tt) 386.03/118.04
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 386.03/118.04
active(isNat(s(z0))) → mark(U21(isNat(z0))) 386.03/118.04
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 386.03/118.04
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 386.03/118.04
active(U11(z0, z1)) → U11(active(z0), z1) 386.03/118.04
active(U12(z0)) → U12(active(z0)) 386.03/118.04
active(U21(z0)) → U21(active(z0)) 386.03/118.04
active(U31(z0, z1)) → U31(active(z0), z1) 386.03/118.04
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 386.03/118.04
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 386.03/118.04
active(s(z0)) → s(active(z0)) 386.03/118.04
active(plus(z0, z1)) → plus(active(z0), z1) 386.03/118.04
active(plus(z0, z1)) → plus(z0, active(z1)) 386.03/118.04
U11(mark(z0), z1) → mark(U11(z0, z1)) 386.03/118.04
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 386.03/118.04
U12(mark(z0)) → mark(U12(z0)) 386.03/118.04
U12(ok(z0)) → ok(U12(z0)) 386.03/118.04
U21(mark(z0)) → mark(U21(z0)) 386.03/118.04
U21(ok(z0)) → ok(U21(z0)) 386.03/118.04
U31(mark(z0), z1) → mark(U31(z0, z1)) 386.03/118.04
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 386.03/118.04
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 386.03/118.04
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 386.03/118.04
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 386.03/118.04
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 386.03/118.04
s(mark(z0)) → mark(s(z0)) 386.03/118.04
s(ok(z0)) → ok(s(z0)) 386.03/118.04
plus(mark(z0), z1) → mark(plus(z0, z1)) 386.03/118.04
plus(z0, mark(z1)) → mark(plus(z0, z1)) 386.03/118.04
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 386.03/118.04
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 386.03/118.04
proper(tt) → ok(tt) 386.03/118.04
proper(U12(z0)) → U12(proper(z0)) 386.03/118.04
proper(isNat(z0)) → isNat(proper(z0)) 386.03/118.04
proper(U21(z0)) → U21(proper(z0)) 386.03/118.04
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 386.03/118.04
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 386.03/118.04
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 386.03/118.04
proper(s(z0)) → s(proper(z0)) 386.03/118.04
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 386.03/118.04
proper(0) → ok(0) 386.03/118.04
isNat(ok(z0)) → ok(isNat(z0)) 386.03/118.04
top(mark(z0)) → top(proper(z0)) 386.03/118.04
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.04
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.04
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.04
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.04
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.04
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.04
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.04
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.04
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.04
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.04
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.04
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.04
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.04
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.04
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.04
S(mark(z0)) → c32(S(z0)) 386.03/118.04
S(ok(z0)) → c33(S(z0)) 386.03/118.04
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.04
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.04
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.04
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.04
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.04
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.04
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.04
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.04
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.04
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.04
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.04
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.04
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.04
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.04
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.04
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.04
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.05
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.05
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.05
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.05
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.05
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.05
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.05
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.05
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.05
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.05
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.05
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.05
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 386.03/118.05
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 386.03/118.05
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 386.03/118.05
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 386.03/118.05
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U31(U41(tt, z0, z1), x1)) → c14(U31'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 386.03/118.05
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 386.03/118.05
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 386.03/118.05
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.05
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.05
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 386.03/118.05
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.05
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.05
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U41(U11(tt, z0), x1, x2)) → c15(U41'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2), ACTIVE(U12(tt))) 386.03/118.05
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2), ACTIVE(U21(tt))) 386.03/118.05
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2), ACTIVE(U31(tt, z0))) 386.03/118.05
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c15(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c15(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2), ACTIVE(isNat(0))) 386.03/118.05
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c15(U41'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c15(U41'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
S tuples:

ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.05
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.05
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.05
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.05
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.05
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.05
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.05
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.05
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.05
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.05
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.05
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.05
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.05
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.05
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.05
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.05
S(mark(z0)) → c32(S(z0)) 386.03/118.05
S(ok(z0)) → c33(S(z0)) 386.03/118.05
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.05
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.05
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.05
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.05
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.05
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.05
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.05
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.05
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.05
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.05
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.05
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.05
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.05
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.05
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.05
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.05
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.05
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.05
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.05
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.05
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.05
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.05
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.05
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.05
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.05
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.05
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.05
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.05
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.05
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.05
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.05
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.05
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.05
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.05
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.05
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.05
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.05
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.05
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.05
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 386.03/118.05
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 386.03/118.05
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 386.03/118.05
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 386.03/118.05
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U31(U41(tt, z0, z1), x1)) → c14(U31'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 386.03/118.05
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 386.03/118.05
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 386.03/118.05
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.05
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.05
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 386.03/118.05
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.05
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.05
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U41(U11(tt, z0), x1, x2)) → c15(U41'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2), ACTIVE(U12(tt))) 386.03/118.05
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2), ACTIVE(U21(tt))) 386.03/118.05
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2), ACTIVE(U31(tt, z0))) 386.03/118.05
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c15(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c15(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2), ACTIVE(isNat(0))) 386.03/118.05
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c15(U41'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c15(U41'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15

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

Removed 4 trailing tuple parts
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386.03/118.05

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 386.03/118.05
active(U12(tt)) → mark(tt) 386.03/118.05
active(U21(tt)) → mark(tt) 386.03/118.05
active(U31(tt, z0)) → mark(z0) 386.03/118.05
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 386.03/118.05
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 386.03/118.05
active(isNat(0)) → mark(tt) 386.03/118.05
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 386.03/118.05
active(isNat(s(z0))) → mark(U21(isNat(z0))) 386.03/118.05
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 386.03/118.05
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 386.03/118.05
active(U11(z0, z1)) → U11(active(z0), z1) 386.03/118.05
active(U12(z0)) → U12(active(z0)) 386.03/118.05
active(U21(z0)) → U21(active(z0)) 386.03/118.05
active(U31(z0, z1)) → U31(active(z0), z1) 386.03/118.05
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 386.03/118.05
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 386.03/118.05
active(s(z0)) → s(active(z0)) 386.03/118.05
active(plus(z0, z1)) → plus(active(z0), z1) 386.03/118.05
active(plus(z0, z1)) → plus(z0, active(z1)) 386.03/118.05
U11(mark(z0), z1) → mark(U11(z0, z1)) 386.03/118.05
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 386.03/118.05
U12(mark(z0)) → mark(U12(z0)) 386.03/118.05
U12(ok(z0)) → ok(U12(z0)) 386.03/118.05
U21(mark(z0)) → mark(U21(z0)) 386.03/118.05
U21(ok(z0)) → ok(U21(z0)) 386.03/118.05
U31(mark(z0), z1) → mark(U31(z0, z1)) 386.03/118.05
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 386.03/118.05
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 386.03/118.05
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 386.03/118.05
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 386.03/118.05
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 386.03/118.05
s(mark(z0)) → mark(s(z0)) 386.03/118.05
s(ok(z0)) → ok(s(z0)) 386.03/118.05
plus(mark(z0), z1) → mark(plus(z0, z1)) 386.03/118.05
plus(z0, mark(z1)) → mark(plus(z0, z1)) 386.03/118.05
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 386.03/118.05
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 386.03/118.05
proper(tt) → ok(tt) 386.03/118.05
proper(U12(z0)) → U12(proper(z0)) 386.03/118.05
proper(isNat(z0)) → isNat(proper(z0)) 386.03/118.05
proper(U21(z0)) → U21(proper(z0)) 386.03/118.05
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 386.03/118.05
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 386.03/118.05
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 386.03/118.05
proper(s(z0)) → s(proper(z0)) 386.03/118.05
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 386.03/118.05
proper(0) → ok(0) 386.03/118.05
isNat(ok(z0)) → ok(isNat(z0)) 386.03/118.05
top(mark(z0)) → top(proper(z0)) 386.03/118.05
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 386.03/118.05
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 386.03/118.05
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 386.03/118.05
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 386.03/118.05
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 386.03/118.05
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 386.03/118.05
U12'(mark(z0)) → c22(U12'(z0)) 386.03/118.05
U12'(ok(z0)) → c23(U12'(z0)) 386.03/118.05
U21'(mark(z0)) → c24(U21'(z0)) 386.03/118.05
U21'(ok(z0)) → c25(U21'(z0)) 386.03/118.05
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 386.03/118.05
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 386.03/118.05
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 386.03/118.05
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 386.03/118.05
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 386.03/118.05
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 386.03/118.05
S(mark(z0)) → c32(S(z0)) 386.03/118.05
S(ok(z0)) → c33(S(z0)) 386.03/118.05
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 386.03/118.05
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 386.03/118.05
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 386.03/118.05
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.05
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 386.03/118.05
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 386.03/118.05
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 386.03/118.05
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.05
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.05
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 386.03/118.05
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 386.03/118.05
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 386.03/118.05
ISNAT(ok(z0)) → c48(ISNAT(z0)) 386.03/118.05
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 386.03/118.05
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 386.03/118.05
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 386.03/118.05
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 386.03/118.05
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 386.03/118.05
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 386.03/118.05
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 386.03/118.05
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 386.03/118.05
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 386.03/118.05
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 386.03/118.05
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 386.03/118.05
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 386.03/118.05
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 386.03/118.05
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 386.03/118.05
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.05
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.05
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.05
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 386.03/118.05
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 386.03/118.05
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 386.03/118.05
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 386.03/118.05
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 386.03/118.05
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 386.03/118.05
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 386.03/118.05
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 386.03/118.05
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 386.03/118.05
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 386.03/118.05
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 386.03/118.05
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 386.03/118.05
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 386.03/118.05
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U31(U41(tt, z0, z1), x1)) → c14(U31'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 386.03/118.05
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 386.03/118.05
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 386.03/118.05
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 386.03/118.05
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 386.03/118.05
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 386.03/118.05
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 386.03/118.05
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 386.03/118.05
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 386.03/118.05
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 386.03/118.05
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 386.03/118.05
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 386.03/118.05
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.05
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.05
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 386.03/118.05
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 386.03/118.05
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 386.03/118.05
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 386.03/118.05
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U41(U11(tt, z0), x1, x2)) → c15(U41'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0))) 386.03/118.05
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c15(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 386.03/118.05
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c15(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 386.03/118.05
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c15(U41'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 386.03/118.05
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c15(U41'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0)))) 386.03/118.05
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 386.03/118.05
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.61
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.61
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.61
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.61
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.61
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.61
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.61
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.61
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.61
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.61
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.61
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.61
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.61
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2))
S tuples:

ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 388.36/118.61
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 388.36/118.61
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.61
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.61
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.61
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.61
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.61
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.61
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.61
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.61
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.61
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.61
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.61
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.61
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.61
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.61
S(mark(z0)) → c32(S(z0)) 388.36/118.61
S(ok(z0)) → c33(S(z0)) 388.36/118.61
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.61
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.61
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.61
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.61
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.61
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.61
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.61
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.61
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.61
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.61
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.61
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.61
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.61
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.61
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.61
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.61
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.61
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.61
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.61
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.61
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.61
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.61
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.61
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.61
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.61
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.61
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.61
ACTIVE(U11(U41(tt, z0, z1), x1)) → c11(U11'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 388.36/118.61
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.61
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.61
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.61
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.61
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.61
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.61
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.61
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.61
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.61
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.61
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.61
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.61
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.61
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.61
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.61
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.61
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.61
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.61
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.61
ACTIVE(U12(U41(tt, z0, z1))) → c12(U12'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 388.36/118.61
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.61
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.61
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.61
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.61
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.61
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.61
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.61
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.61
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.61
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.61
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.61
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.61
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.61
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.61
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.61
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.61
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.61
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.61
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.61
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.61
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.61
ACTIVE(U21(U41(tt, z0, z1))) → c13(U21'(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 388.36/118.61
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.61
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.61
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.61
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.61
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.61
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.61
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.61
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.61
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.61
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.61
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.61
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.61
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.61
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.61
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.61
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.61
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.61
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.61
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.61
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.61
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.61
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.61
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.61
ACTIVE(U31(U41(tt, z0, z1), x1)) → c14(U31'(mark(U42(isNat(z1), z0, z1)), x1), ACTIVE(U41(tt, z0, z1))) 388.36/118.61
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.61
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.61
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.61
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.61
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.61
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.61
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.61
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.61
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.61
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.61
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.61
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.61
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.61
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.61
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.61
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.61
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.61
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.62
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.62
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.62
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.62
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.62
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.62
ACTIVE(U41(U11(tt, z0), x1, x2)) → c15(U41'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c15(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c15(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c15(U41'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c15(U41'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0)))) 388.36/118.62
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.62
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.62
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.62
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15

388.36/118.62
388.36/118.62

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

Split RHS of tuples not part of any SCC
388.36/118.62
388.36/118.62

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.62
active(U12(tt)) → mark(tt) 388.36/118.62
active(U21(tt)) → mark(tt) 388.36/118.62
active(U31(tt, z0)) → mark(z0) 388.36/118.62
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.62
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.62
active(isNat(0)) → mark(tt) 388.36/118.62
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.62
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.62
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.62
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.62
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.62
active(U12(z0)) → U12(active(z0)) 388.36/118.62
active(U21(z0)) → U21(active(z0)) 388.36/118.62
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.62
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.62
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.62
active(s(z0)) → s(active(z0)) 388.36/118.62
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.62
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.62
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.62
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.62
U12(mark(z0)) → mark(U12(z0)) 388.36/118.62
U12(ok(z0)) → ok(U12(z0)) 388.36/118.62
U21(mark(z0)) → mark(U21(z0)) 388.36/118.62
U21(ok(z0)) → ok(U21(z0)) 388.36/118.62
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.62
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.62
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.62
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.62
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.62
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.62
s(mark(z0)) → mark(s(z0)) 388.36/118.62
s(ok(z0)) → ok(s(z0)) 388.36/118.62
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.62
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.62
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.62
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.62
proper(tt) → ok(tt) 388.36/118.62
proper(U12(z0)) → U12(proper(z0)) 388.36/118.62
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.62
proper(U21(z0)) → U21(proper(z0)) 388.36/118.62
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.62
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.62
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.62
proper(s(z0)) → s(proper(z0)) 388.36/118.62
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.62
proper(0) → ok(0) 388.36/118.62
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.62
top(mark(z0)) → top(proper(z0)) 388.36/118.62
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 388.36/118.62
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 388.36/118.62
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.62
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.62
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.62
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.62
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.62
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.62
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.62
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.62
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.62
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.62
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.62
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.62
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.62
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.62
S(mark(z0)) → c32(S(z0)) 388.36/118.62
S(ok(z0)) → c33(S(z0)) 388.36/118.62
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.62
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.62
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.62
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.62
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.62
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.62
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.62
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.62
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.62
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.62
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.62
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.62
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.62
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.62
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.62
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.62
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.62
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.62
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.62
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.62
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.62
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.62
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.62
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.62
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.62
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.62
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.62
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.62
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.62
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.62
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.62
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.62
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.62
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.62
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.62
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.62
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.62
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.62
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.62
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.62
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.62
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.62
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.62
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.62
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.62
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.62
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.62
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.62
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.62
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.62
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.62
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.62
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.62
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.62
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.62
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c15(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.62
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.62
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.62
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.62
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.62
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.62
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.62
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.62
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.62
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.62
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.62
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.62
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0))))
S tuples:

ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) 388.36/118.62
ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 388.36/118.62
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.62
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.62
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.62
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.62
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.62
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.62
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.62
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.62
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.62
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.62
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.62
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.62
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.62
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.62
S(mark(z0)) → c32(S(z0)) 388.36/118.62
S(ok(z0)) → c33(S(z0)) 388.36/118.62
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.62
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.62
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.62
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.62
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.62
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.62
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.62
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.62
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.62
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.62
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.62
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.62
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.62
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.62
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.62
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.62
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.62
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.62
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.62
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.62
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.62
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.62
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.62
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.62
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.62
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.62
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.62
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.62
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.62
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.62
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.62
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.62
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.62
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.62
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.62
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.62
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.62
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.62
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.62
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.62
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.62
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.62
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.62
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.62
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.62
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.62
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.62
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.62
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.62
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.62
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.62
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.62
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.62
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.62
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.62
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c15(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.62
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.62
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.62
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.62
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.62
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.62
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.62
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.62
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.62
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.62
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.62
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.62
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0))))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5

388.36/118.62
388.36/118.62

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

Use narrowing to replace ACTIVE(U42(z0, z1, z2)) → c16(U42'(active(z0), z1, z2), ACTIVE(z0)) by

ACTIVE(U42(U11(tt, z0), x1, x2)) → c16(U42'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0))) 388.36/118.62
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2), ACTIVE(U12(tt))) 388.36/118.62
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2), ACTIVE(U21(tt))) 388.36/118.62
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2), ACTIVE(U31(tt, z0))) 388.36/118.62
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c16(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 388.36/118.62
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c16(U42'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2), ACTIVE(isNat(0))) 388.36/118.62
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c16(U42'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 388.36/118.62
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c16(U42'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0)))) 388.36/118.62
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.62
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.62
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.62
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.62
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.62
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.62
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.62
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
388.36/118.62
388.36/118.62

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.62
active(U12(tt)) → mark(tt) 388.36/118.62
active(U21(tt)) → mark(tt) 388.36/118.62
active(U31(tt, z0)) → mark(z0) 388.36/118.62
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.62
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.62
active(isNat(0)) → mark(tt) 388.36/118.62
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.62
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.62
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.62
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.62
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.62
active(U12(z0)) → U12(active(z0)) 388.36/118.62
active(U21(z0)) → U21(active(z0)) 388.36/118.62
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.62
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.62
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.62
active(s(z0)) → s(active(z0)) 388.36/118.62
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.62
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.62
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.62
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.62
U12(mark(z0)) → mark(U12(z0)) 388.36/118.62
U12(ok(z0)) → ok(U12(z0)) 388.36/118.62
U21(mark(z0)) → mark(U21(z0)) 388.36/118.62
U21(ok(z0)) → ok(U21(z0)) 388.36/118.62
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.62
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.62
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.62
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.62
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.62
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.62
s(mark(z0)) → mark(s(z0)) 388.36/118.62
s(ok(z0)) → ok(s(z0)) 388.36/118.62
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.62
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.62
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.62
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.62
proper(tt) → ok(tt) 388.36/118.62
proper(U12(z0)) → U12(proper(z0)) 388.36/118.62
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.62
proper(U21(z0)) → U21(proper(z0)) 388.36/118.62
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.62
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.62
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.62
proper(s(z0)) → s(proper(z0)) 388.36/118.62
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.62
proper(0) → ok(0) 388.36/118.62
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.62
top(mark(z0)) → top(proper(z0)) 388.36/118.62
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 388.36/118.62
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.62
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.62
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.62
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.62
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.62
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.62
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.62
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.62
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.62
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.62
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.62
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.62
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.62
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.62
S(mark(z0)) → c32(S(z0)) 388.36/118.62
S(ok(z0)) → c33(S(z0)) 388.36/118.62
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.62
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.62
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.62
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.62
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.62
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.62
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.62
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.62
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.62
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.62
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.62
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.62
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.62
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.62
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.62
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.62
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.62
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.62
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.62
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.62
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.62
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.62
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.62
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.62
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.62
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.62
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.62
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.62
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.63
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.63
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.63
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.63
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.63
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.63
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.63
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.63
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.63
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.63
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.63
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.63
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c15(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.63
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.63
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.63
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.63
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.63
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.63
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U42(U11(tt, z0), x1, x2)) → c16(U42'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2), ACTIVE(U12(tt))) 388.36/118.63
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2), ACTIVE(U21(tt))) 388.36/118.63
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2), ACTIVE(U31(tt, z0))) 388.36/118.63
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c16(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c16(U42'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2), ACTIVE(isNat(0))) 388.36/118.63
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c16(U42'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c16(U42'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
S tuples:

ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 388.36/118.63
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.63
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.63
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.63
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.63
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.63
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.63
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.63
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.63
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.63
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.63
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.63
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.63
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.63
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.63
S(mark(z0)) → c32(S(z0)) 388.36/118.63
S(ok(z0)) → c33(S(z0)) 388.36/118.63
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.63
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.63
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.63
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.63
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.63
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.63
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.63
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.63
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.63
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.63
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.63
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.63
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.63
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.63
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.63
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.63
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.63
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.63
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.63
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.63
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.63
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.63
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.63
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.63
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.63
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.63
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.63
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.63
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.63
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c15(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.63
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.63
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.63
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.63
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.63
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.63
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U42(U11(tt, z0), x1, x2)) → c16(U42'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2), ACTIVE(U12(tt))) 388.36/118.63
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2), ACTIVE(U21(tt))) 388.36/118.63
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2), ACTIVE(U31(tt, z0))) 388.36/118.63
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c16(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c16(U42'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2), ACTIVE(isNat(0))) 388.36/118.63
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c16(U42'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c16(U42'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16

388.36/118.63
388.36/118.63

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

Removed 4 trailing tuple parts
388.36/118.63
388.36/118.63

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.63
active(U12(tt)) → mark(tt) 388.36/118.63
active(U21(tt)) → mark(tt) 388.36/118.63
active(U31(tt, z0)) → mark(z0) 388.36/118.63
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.63
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.63
active(isNat(0)) → mark(tt) 388.36/118.63
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.63
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.63
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.63
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.63
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.63
active(U12(z0)) → U12(active(z0)) 388.36/118.63
active(U21(z0)) → U21(active(z0)) 388.36/118.63
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.63
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.63
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.63
active(s(z0)) → s(active(z0)) 388.36/118.63
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.63
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.63
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.63
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.63
U12(mark(z0)) → mark(U12(z0)) 388.36/118.63
U12(ok(z0)) → ok(U12(z0)) 388.36/118.63
U21(mark(z0)) → mark(U21(z0)) 388.36/118.63
U21(ok(z0)) → ok(U21(z0)) 388.36/118.63
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.63
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.63
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.63
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.63
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.63
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.63
s(mark(z0)) → mark(s(z0)) 388.36/118.63
s(ok(z0)) → ok(s(z0)) 388.36/118.63
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.63
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.63
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.63
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.63
proper(tt) → ok(tt) 388.36/118.63
proper(U12(z0)) → U12(proper(z0)) 388.36/118.63
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.63
proper(U21(z0)) → U21(proper(z0)) 388.36/118.63
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.63
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.63
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.63
proper(s(z0)) → s(proper(z0)) 388.36/118.63
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.63
proper(0) → ok(0) 388.36/118.63
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.63
top(mark(z0)) → top(proper(z0)) 388.36/118.63
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 388.36/118.63
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.63
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.63
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.63
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.63
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.63
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.63
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.63
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.63
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.63
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.63
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.63
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.63
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.63
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.63
S(mark(z0)) → c32(S(z0)) 388.36/118.63
S(ok(z0)) → c33(S(z0)) 388.36/118.63
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.63
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.63
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.63
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.63
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.63
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.63
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.63
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.63
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.63
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.63
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.63
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.63
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.63
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.63
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.63
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.63
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.63
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.63
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.63
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.63
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.63
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.63
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.63
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.63
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.63
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.63
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.63
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.63
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.63
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c15(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.63
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.63
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.63
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.63
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.63
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.63
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U42(U11(tt, z0), x1, x2)) → c16(U42'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c16(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c16(U42'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c16(U42'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c16(U42'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.63
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2))
S tuples:

ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 388.36/118.63
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.63
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.63
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.63
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.63
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.63
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.63
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.63
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.63
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.63
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.63
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.63
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.63
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.63
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.63
S(mark(z0)) → c32(S(z0)) 388.36/118.63
S(ok(z0)) → c33(S(z0)) 388.36/118.63
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.63
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.63
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.63
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.63
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.63
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.63
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.63
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.63
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.63
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.63
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.63
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.63
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.63
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.63
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.63
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.63
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.63
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(U11(U42(tt, z0, z1), x1)) → c11(U11'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.63
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U12(U42(tt, z0, z1))) → c12(U12'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.63
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.63
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.63
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U21(U42(tt, z0, z1))) → c13(U21'(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.63
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.63
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.63
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U31(U42(tt, z0, z1), x1)) → c14(U31'(mark(s(plus(z1, z0))), x1), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.63
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.63
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.63
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.63
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.63
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c15(U41'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.63
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.63
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.63
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.63
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.63
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.63
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.63
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U42(U11(tt, z0), x1, x2)) → c16(U42'(mark(U12(isNat(z0))), x1, x2), ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c16(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2), ACTIVE(U41(tt, z0, z1))) 388.36/118.63
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c16(U42'(mark(s(plus(z1, z0))), x1, x2), ACTIVE(U42(tt, z0, z1))) 388.36/118.63
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c16(U42'(mark(U11(isNat(z0), z1)), x1, x2), ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c16(U42'(mark(U21(isNat(z0))), x1, x2), ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.63
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.63
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16

388.36/118.63
388.36/118.63

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

Split RHS of tuples not part of any SCC
388.36/118.63
388.36/118.63

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.63
active(U12(tt)) → mark(tt) 388.36/118.63
active(U21(tt)) → mark(tt) 388.36/118.63
active(U31(tt, z0)) → mark(z0) 388.36/118.63
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.63
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.63
active(isNat(0)) → mark(tt) 388.36/118.63
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.63
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.63
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.63
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.63
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.63
active(U12(z0)) → U12(active(z0)) 388.36/118.63
active(U21(z0)) → U21(active(z0)) 388.36/118.63
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.63
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.63
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.63
active(s(z0)) → s(active(z0)) 388.36/118.63
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.63
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.63
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.63
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.63
U12(mark(z0)) → mark(U12(z0)) 388.36/118.63
U12(ok(z0)) → ok(U12(z0)) 388.36/118.63
U21(mark(z0)) → mark(U21(z0)) 388.36/118.63
U21(ok(z0)) → ok(U21(z0)) 388.36/118.63
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.63
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.63
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.63
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.63
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.63
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.63
s(mark(z0)) → mark(s(z0)) 388.36/118.63
s(ok(z0)) → ok(s(z0)) 388.36/118.63
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.63
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.63
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.63
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.63
proper(tt) → ok(tt) 388.36/118.63
proper(U12(z0)) → U12(proper(z0)) 388.36/118.63
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.63
proper(U21(z0)) → U21(proper(z0)) 388.36/118.63
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.63
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.63
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.63
proper(s(z0)) → s(proper(z0)) 388.36/118.63
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.63
proper(0) → ok(0) 388.36/118.63
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.63
top(mark(z0)) → top(proper(z0)) 388.36/118.63
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 388.36/118.63
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.63
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.63
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.63
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.63
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.63
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.63
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.63
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.63
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.63
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.63
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.63
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.63
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.63
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.63
S(mark(z0)) → c32(S(z0)) 388.36/118.63
S(ok(z0)) → c33(S(z0)) 388.36/118.63
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.63
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.63
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.63
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.63
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.63
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.63
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.63
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.63
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.63
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.63
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.63
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.63
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.63
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.63
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.63
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.63
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.63
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.63
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.63
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.63
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.63
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.63
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.63
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.63
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.63
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.63
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.63
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.63
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.63
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.63
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.63
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.63
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.63
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.63
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.63
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.63
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.63
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.63
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.63
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.63
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.63
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.63
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.63
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.63
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.63
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.63
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.63
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.63
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.63
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.63
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.64
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.64
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.64
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.64
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.64
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.64
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.64
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.64
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.64
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.64
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.64
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.64
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.64
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.64
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.64
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.64
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.64
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.64
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.64
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.64
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.64
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.64
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.64
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.64
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.64
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.64
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.64
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.64
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.64
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.64
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.64
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.64
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.64
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.64
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.64
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.64
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.64
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.64
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.64
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.64
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.64
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0))))
S tuples:

ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) 388.36/118.64
ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.64
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.64
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.64
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.64
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.64
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.64
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.64
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.64
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.64
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.64
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.64
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.64
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.64
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.64
S(mark(z0)) → c32(S(z0)) 388.36/118.64
S(ok(z0)) → c33(S(z0)) 388.36/118.64
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.64
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.64
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.64
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.64
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.64
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.64
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.64
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.64
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.64
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.64
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.64
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.64
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.64
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.64
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.64
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.64
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.64
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.64
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.64
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.64
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.64
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.64
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.64
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.64
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.64
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.64
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.64
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.64
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.64
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.64
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.64
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.64
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.64
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.64
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.64
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.64
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.64
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.64
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.64
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.64
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.64
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.64
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.64
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.64
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.64
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.64
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.64
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.64
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.64
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.64
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.64
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.64
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.64
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.64
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.64
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.64
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.64
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.64
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.64
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.64
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.64
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.64
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.64
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.64
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.64
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.64
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.64
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.64
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.64
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.64
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.64
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.64
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.64
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.64
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.64
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.64
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.64
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.64
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.64
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.64
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.64
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.64
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.64
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.64
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.64
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.64
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.64
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.64
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.64
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.64
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.64
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.64
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.64
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.64
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.64
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.64
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.64
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.64
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.64
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.64
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.64
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.64
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.64
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.64
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.64
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.64
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.64
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.64
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.64
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.64
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.64
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.64
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.64
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.64
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.64
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.64
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.64
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.64
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.64
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.64
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.64
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.64
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.64
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.64
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.64
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.64
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.64
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.64
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.64
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.64
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.64
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.64
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.64
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.64
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.64
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.64
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.64
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.64
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.64
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.64
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.64
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.64
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.64
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.64
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.64
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.64
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.64
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.64
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.64
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.64
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0))))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6

388.36/118.64
388.36/118.64

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

Use narrowing to replace ACTIVE(s(z0)) → c17(S(active(z0)), ACTIVE(z0)) by

ACTIVE(s(U11(tt, z0))) → c17(S(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 388.36/118.64
ACTIVE(s(U12(tt))) → c17(S(mark(tt)), ACTIVE(U12(tt))) 388.36/118.65
ACTIVE(s(U21(tt))) → c17(S(mark(tt)), ACTIVE(U21(tt))) 388.36/118.65
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0)), ACTIVE(U31(tt, z0))) 388.36/118.65
ACTIVE(s(U41(tt, z0, z1))) → c17(S(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(s(U42(tt, z0, z1))) → c17(S(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(s(isNat(0))) → c17(S(mark(tt)), ACTIVE(isNat(0))) 388.36/118.65
ACTIVE(s(isNat(plus(z0, z1)))) → c17(S(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(s(isNat(s(z0)))) → c17(S(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
388.36/118.65
388.36/118.65

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.65
active(U12(tt)) → mark(tt) 388.36/118.65
active(U21(tt)) → mark(tt) 388.36/118.65
active(U31(tt, z0)) → mark(z0) 388.36/118.65
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.65
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.65
active(isNat(0)) → mark(tt) 388.36/118.65
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.65
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.65
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.65
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.65
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.65
active(U12(z0)) → U12(active(z0)) 388.36/118.65
active(U21(z0)) → U21(active(z0)) 388.36/118.65
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.65
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.65
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.65
active(s(z0)) → s(active(z0)) 388.36/118.65
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.65
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.65
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.65
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.65
U12(mark(z0)) → mark(U12(z0)) 388.36/118.65
U12(ok(z0)) → ok(U12(z0)) 388.36/118.65
U21(mark(z0)) → mark(U21(z0)) 388.36/118.65
U21(ok(z0)) → ok(U21(z0)) 388.36/118.65
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.65
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.65
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.65
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.65
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.65
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.65
s(mark(z0)) → mark(s(z0)) 388.36/118.65
s(ok(z0)) → ok(s(z0)) 388.36/118.65
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.65
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.65
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.65
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.65
proper(tt) → ok(tt) 388.36/118.65
proper(U12(z0)) → U12(proper(z0)) 388.36/118.65
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.65
proper(U21(z0)) → U21(proper(z0)) 388.36/118.65
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.65
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.65
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.65
proper(s(z0)) → s(proper(z0)) 388.36/118.65
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.65
proper(0) → ok(0) 388.36/118.65
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.65
top(mark(z0)) → top(proper(z0)) 388.36/118.65
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.65
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.65
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.65
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.65
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.65
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.65
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.65
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.65
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.65
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.65
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.65
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.65
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.65
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.65
S(mark(z0)) → c32(S(z0)) 388.36/118.65
S(ok(z0)) → c33(S(z0)) 388.36/118.65
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.65
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.65
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.65
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.65
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.65
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.65
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.65
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.65
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.65
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.65
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.65
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.65
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.65
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.65
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.65
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.65
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.65
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.65
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.65
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.65
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.65
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.65
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.65
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.65
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.65
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.65
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.65
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.65
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.65
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.65
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.65
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.65
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.65
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.65
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.65
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.65
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.65
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.65
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.65
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(s(U11(tt, z0))) → c17(S(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(s(U12(tt))) → c17(S(mark(tt)), ACTIVE(U12(tt))) 388.36/118.65
ACTIVE(s(U21(tt))) → c17(S(mark(tt)), ACTIVE(U21(tt))) 388.36/118.65
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0)), ACTIVE(U31(tt, z0))) 388.36/118.65
ACTIVE(s(U41(tt, z0, z1))) → c17(S(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(s(U42(tt, z0, z1))) → c17(S(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(s(isNat(0))) → c17(S(mark(tt)), ACTIVE(isNat(0))) 388.36/118.65
ACTIVE(s(isNat(plus(z0, z1)))) → c17(S(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(s(isNat(s(z0)))) → c17(S(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.65
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.65
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.65
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.65
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.65
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.65
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.65
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.65
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.65
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.65
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.65
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.65
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.65
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.65
S(mark(z0)) → c32(S(z0)) 388.36/118.65
S(ok(z0)) → c33(S(z0)) 388.36/118.65
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.65
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.65
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.65
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.65
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.65
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.65
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.65
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.65
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.65
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.65
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.65
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.65
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.65
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.65
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.65
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.65
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.65
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.65
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.65
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.65
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.65
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.65
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.65
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.65
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.65
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.65
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.65
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.65
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.65
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.65
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.65
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.65
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.65
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.65
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.65
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.65
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.65
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.65
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.65
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(s(U11(tt, z0))) → c17(S(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(s(U12(tt))) → c17(S(mark(tt)), ACTIVE(U12(tt))) 388.36/118.65
ACTIVE(s(U21(tt))) → c17(S(mark(tt)), ACTIVE(U21(tt))) 388.36/118.65
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0)), ACTIVE(U31(tt, z0))) 388.36/118.65
ACTIVE(s(U41(tt, z0, z1))) → c17(S(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(s(U42(tt, z0, z1))) → c17(S(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(s(isNat(0))) → c17(S(mark(tt)), ACTIVE(isNat(0))) 388.36/118.65
ACTIVE(s(isNat(plus(z0, z1)))) → c17(S(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(s(isNat(s(z0)))) → c17(S(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17

388.36/118.65
388.36/118.65

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

Removed 4 trailing tuple parts
388.36/118.65
388.36/118.65

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.65
active(U12(tt)) → mark(tt) 388.36/118.65
active(U21(tt)) → mark(tt) 388.36/118.65
active(U31(tt, z0)) → mark(z0) 388.36/118.65
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.65
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.65
active(isNat(0)) → mark(tt) 388.36/118.65
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.65
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.65
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.65
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.65
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.65
active(U12(z0)) → U12(active(z0)) 388.36/118.65
active(U21(z0)) → U21(active(z0)) 388.36/118.65
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.65
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.65
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.65
active(s(z0)) → s(active(z0)) 388.36/118.65
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.65
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.65
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.65
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.65
U12(mark(z0)) → mark(U12(z0)) 388.36/118.65
U12(ok(z0)) → ok(U12(z0)) 388.36/118.65
U21(mark(z0)) → mark(U21(z0)) 388.36/118.65
U21(ok(z0)) → ok(U21(z0)) 388.36/118.65
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.65
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.65
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.65
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.65
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.65
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.65
s(mark(z0)) → mark(s(z0)) 388.36/118.65
s(ok(z0)) → ok(s(z0)) 388.36/118.65
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.65
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.65
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.65
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.65
proper(tt) → ok(tt) 388.36/118.65
proper(U12(z0)) → U12(proper(z0)) 388.36/118.65
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.65
proper(U21(z0)) → U21(proper(z0)) 388.36/118.65
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.65
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.65
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.65
proper(s(z0)) → s(proper(z0)) 388.36/118.65
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.65
proper(0) → ok(0) 388.36/118.65
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.65
top(mark(z0)) → top(proper(z0)) 388.36/118.65
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.65
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.65
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.65
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.65
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.65
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.65
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.65
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.65
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.65
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.65
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.65
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.65
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.65
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.65
S(mark(z0)) → c32(S(z0)) 388.36/118.65
S(ok(z0)) → c33(S(z0)) 388.36/118.65
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.65
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.65
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.65
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.65
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.65
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.65
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.65
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.65
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.65
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.65
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.65
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.65
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.65
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.65
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.65
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.65
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.65
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.65
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.65
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.65
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.65
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.65
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.65
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.65
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.65
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.65
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.65
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.65
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.65
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.65
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.65
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.65
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.65
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.65
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.65
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.65
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.65
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.65
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.65
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(s(U11(tt, z0))) → c17(S(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(s(U41(tt, z0, z1))) → c17(S(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(s(U42(tt, z0, z1))) → c17(S(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(s(isNat(plus(z0, z1)))) → c17(S(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(s(isNat(s(z0)))) → c17(S(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.65
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.65
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.65
ACTIVE(s(isNat(0))) → c17(S(mark(tt)))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.65
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.65
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.65
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.65
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.65
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.65
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.65
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.65
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.65
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.65
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.65
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.65
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.65
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.65
S(mark(z0)) → c32(S(z0)) 388.36/118.65
S(ok(z0)) → c33(S(z0)) 388.36/118.65
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.65
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.65
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.65
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.65
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.65
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.65
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.65
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.65
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.65
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.65
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.65
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.65
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.65
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.65
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.65
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.65
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.65
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.65
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.65
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.65
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.65
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.65
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.65
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.65
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.65
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.65
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.65
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.65
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.65
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.65
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.65
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.65
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.65
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.65
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.65
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.65
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.65
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.65
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.65
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(s(U11(tt, z0))) → c17(S(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(s(U41(tt, z0, z1))) → c17(S(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(s(U42(tt, z0, z1))) → c17(S(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(s(isNat(plus(z0, z1)))) → c17(S(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(s(isNat(s(z0)))) → c17(S(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.65
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.65
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.65
ACTIVE(s(isNat(0))) → c17(S(mark(tt)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17

388.36/118.65
388.36/118.65

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

Split RHS of tuples not part of any SCC
388.36/118.65
388.36/118.65

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.65
active(U12(tt)) → mark(tt) 388.36/118.65
active(U21(tt)) → mark(tt) 388.36/118.65
active(U31(tt, z0)) → mark(z0) 388.36/118.65
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.65
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.65
active(isNat(0)) → mark(tt) 388.36/118.65
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.65
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.65
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.65
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.65
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.65
active(U12(z0)) → U12(active(z0)) 388.36/118.65
active(U21(z0)) → U21(active(z0)) 388.36/118.65
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.65
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.65
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.65
active(s(z0)) → s(active(z0)) 388.36/118.65
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.65
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.65
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.65
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.65
U12(mark(z0)) → mark(U12(z0)) 388.36/118.65
U12(ok(z0)) → ok(U12(z0)) 388.36/118.65
U21(mark(z0)) → mark(U21(z0)) 388.36/118.65
U21(ok(z0)) → ok(U21(z0)) 388.36/118.65
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.65
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.65
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.65
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.65
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.65
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.65
s(mark(z0)) → mark(s(z0)) 388.36/118.65
s(ok(z0)) → ok(s(z0)) 388.36/118.65
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.65
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.65
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.65
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.65
proper(tt) → ok(tt) 388.36/118.65
proper(U12(z0)) → U12(proper(z0)) 388.36/118.65
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.65
proper(U21(z0)) → U21(proper(z0)) 388.36/118.65
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.65
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.65
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.65
proper(s(z0)) → s(proper(z0)) 388.36/118.65
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.65
proper(0) → ok(0) 388.36/118.65
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.65
top(mark(z0)) → top(proper(z0)) 388.36/118.65
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.65
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.65
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.65
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.65
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.65
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.65
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.65
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.65
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.65
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.65
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.65
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.65
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.65
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.65
S(mark(z0)) → c32(S(z0)) 388.36/118.65
S(ok(z0)) → c33(S(z0)) 388.36/118.65
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.65
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.65
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.65
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.65
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.65
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.65
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.65
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.65
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.65
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.65
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.65
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.65
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.65
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.65
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.65
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.65
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.65
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.65
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.65
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.65
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.65
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.65
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.65
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.65
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.65
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.65
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.65
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.65
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.65
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.65
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.65
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.65
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.65
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.65
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.65
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.65
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.65
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.65
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.65
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.65
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.65
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.65
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.65
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.65
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.65
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.65
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.65
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.65
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.65
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.65
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.65
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.65
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.65
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.65
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.65
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.65
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.65
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.65
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.65
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.65
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.65
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.65
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.65
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.65
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.65
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.65
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.65
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.65
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.65
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.65
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.65
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.65
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.65
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0))))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.65
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.65
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.65
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.65
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.65
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.66
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.66
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.66
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.66
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.66
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.66
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.66
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.66
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.66
S(mark(z0)) → c32(S(z0)) 388.36/118.66
S(ok(z0)) → c33(S(z0)) 388.36/118.66
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.66
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.66
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.66
PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.66
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.66
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.66
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.66
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.66
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.66
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.66
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.66
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.66
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.66
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.66
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.66
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.66
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.66
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.66
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.66
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.66
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.66
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.66
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.66
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.66
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.66
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.66
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.66
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.66
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.66
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.66
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.66
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.66
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.66
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0))))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7

388.36/118.66
388.36/118.66

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

Use narrowing to replace PROPER(U11(z0, z1)) → c37(U11'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.66
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 388.36/118.66
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.66
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.66
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.66
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.66
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.66
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.66
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.66
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.66
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 388.36/118.66
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 388.36/118.66
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.66
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.66
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
388.36/118.66
388.36/118.66

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.66
active(U12(tt)) → mark(tt) 388.36/118.66
active(U21(tt)) → mark(tt) 388.36/118.66
active(U31(tt, z0)) → mark(z0) 388.36/118.66
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.66
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.66
active(isNat(0)) → mark(tt) 388.36/118.66
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.66
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.66
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.66
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.66
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.66
active(U12(z0)) → U12(active(z0)) 388.36/118.66
active(U21(z0)) → U21(active(z0)) 388.36/118.66
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.66
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.66
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.66
active(s(z0)) → s(active(z0)) 388.36/118.66
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.66
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.66
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.66
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.66
U12(mark(z0)) → mark(U12(z0)) 388.36/118.66
U12(ok(z0)) → ok(U12(z0)) 388.36/118.66
U21(mark(z0)) → mark(U21(z0)) 388.36/118.66
U21(ok(z0)) → ok(U21(z0)) 388.36/118.66
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.66
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.66
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.66
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.66
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.66
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.66
s(mark(z0)) → mark(s(z0)) 388.36/118.66
s(ok(z0)) → ok(s(z0)) 388.36/118.66
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.66
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.66
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.66
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.66
proper(tt) → ok(tt) 388.36/118.66
proper(U12(z0)) → U12(proper(z0)) 388.36/118.66
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.66
proper(U21(z0)) → U21(proper(z0)) 388.36/118.66
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.66
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.66
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.66
proper(s(z0)) → s(proper(z0)) 388.36/118.66
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.66
proper(0) → ok(0) 388.36/118.66
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.66
top(mark(z0)) → top(proper(z0)) 388.36/118.66
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.66
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.66
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.66
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.66
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.66
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.66
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.66
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.66
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.66
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.66
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.66
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.66
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.66
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.66
S(mark(z0)) → c32(S(z0)) 388.36/118.66
S(ok(z0)) → c33(S(z0)) 388.36/118.66
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.66
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.66
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.66
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.66
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.66
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.66
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.66
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.66
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.66
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.66
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.66
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.66
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.66
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.66
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.66
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.66
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.66
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.66
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.66
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.66
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.66
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.66
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.66
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.66
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.66
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.66
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.66
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.66
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.66
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.66
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.66
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.66
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.66
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.66
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 388.36/118.66
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.66
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.66
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.66
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.66
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.66
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.66
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.66
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.66
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 388.36/118.66
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 388.36/118.66
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.66
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.66
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.66
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.66
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.66
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.66
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.66
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.66
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.66
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.66
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.66
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.66
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.66
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.66
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.66
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.66
S(mark(z0)) → c32(S(z0)) 388.36/118.66
S(ok(z0)) → c33(S(z0)) 388.36/118.66
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.66
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.66
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.66
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.66
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.66
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.66
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.66
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.66
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.66
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.66
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.66
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.66
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.66
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.66
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.66
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.66
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.66
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.66
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.66
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.66
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.66
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.66
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.66
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.66
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.66
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.66
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.66
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.66
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.66
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.66
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.66
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.66
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.66
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.66
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 388.36/118.66
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.66
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.66
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.66
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.66
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.66
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.66
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.66
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.66
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 388.36/118.66
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 388.36/118.66
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.66
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.66
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37

388.36/118.66
388.36/118.66

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

Removed 4 trailing tuple parts
388.36/118.66
388.36/118.66

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.66
active(U12(tt)) → mark(tt) 388.36/118.66
active(U21(tt)) → mark(tt) 388.36/118.66
active(U31(tt, z0)) → mark(z0) 388.36/118.66
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.66
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.66
active(isNat(0)) → mark(tt) 388.36/118.66
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.66
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.66
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.66
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.66
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.66
active(U12(z0)) → U12(active(z0)) 388.36/118.66
active(U21(z0)) → U21(active(z0)) 388.36/118.66
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.66
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.66
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.66
active(s(z0)) → s(active(z0)) 388.36/118.66
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.66
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.66
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.66
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.66
U12(mark(z0)) → mark(U12(z0)) 388.36/118.66
U12(ok(z0)) → ok(U12(z0)) 388.36/118.66
U21(mark(z0)) → mark(U21(z0)) 388.36/118.66
U21(ok(z0)) → ok(U21(z0)) 388.36/118.66
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.66
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.66
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.66
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.66
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.66
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.66
s(mark(z0)) → mark(s(z0)) 388.36/118.66
s(ok(z0)) → ok(s(z0)) 388.36/118.66
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.66
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.66
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.66
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.66
proper(tt) → ok(tt) 388.36/118.66
proper(U12(z0)) → U12(proper(z0)) 388.36/118.66
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.66
proper(U21(z0)) → U21(proper(z0)) 388.36/118.66
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.66
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.66
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.66
proper(s(z0)) → s(proper(z0)) 388.36/118.66
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.66
proper(0) → ok(0) 388.36/118.66
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.66
top(mark(z0)) → top(proper(z0)) 388.36/118.66
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.66
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.66
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.66
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.66
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.66
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.66
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.66
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.66
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.66
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.66
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.66
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.66
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.66
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.66
S(mark(z0)) → c32(S(z0)) 388.36/118.66
S(ok(z0)) → c33(S(z0)) 388.36/118.66
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.66
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.66
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.66
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.66
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.66
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.66
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.66
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.66
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.66
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.66
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.66
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.66
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.66
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.66
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.66
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.66
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.66
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.66
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.66
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.66
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.66
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.66
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.66
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.66
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.66
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.66
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.66
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.66
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.66
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.66
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.66
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.66
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.66
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.66
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.66
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.66
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.66
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.66
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.66
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.66
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.66
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.66
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.66
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.66
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.66
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.66
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.66
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.66
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.66
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.66
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.66
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.66
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.66
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.66
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.66
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.66
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.66
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.66
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.66
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.66
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.66
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.66
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.66
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.66
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.66
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.66
S(mark(z0)) → c32(S(z0)) 388.36/118.66
S(ok(z0)) → c33(S(z0)) 388.36/118.66
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.66
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.66
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.66
PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.66
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.66
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.66
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.66
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.66
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.66
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.66
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.66
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.66
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.66
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.66
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.66
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.66
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.66
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.66
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.66
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.66
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.66
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.66
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.66
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.66
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.66
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.66
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.66
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.66
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.66
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.66
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.66
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.66
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.66
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.66
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.66
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.66
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.66
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.66
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.66
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.66
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.66
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.66
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.66
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.66
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.66
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.66
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.66
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.66
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.66
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.66
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.66
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.66
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.66
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.66
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.66
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.66
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.67
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.67
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.67
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.67
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.67
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.67
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.67
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.67
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.67
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.67
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.67
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.67
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.67
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.67
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.67
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.67
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.67
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.67
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.67
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c39, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37

388.36/118.67
388.36/118.67

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

Use narrowing to replace PROPER(U12(z0)) → c39(U12'(proper(z0)), PROPER(z0)) by

PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.67
PROPER(U12(tt)) → c39(U12'(ok(tt)), PROPER(tt)) 388.36/118.67
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.67
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.67
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.67
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.67
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.67
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.67
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.67
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.67
PROPER(U12(0)) → c39(U12'(ok(0)), PROPER(0))
388.36/118.67
388.36/118.67

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.67
active(U12(tt)) → mark(tt) 388.36/118.67
active(U21(tt)) → mark(tt) 388.36/118.67
active(U31(tt, z0)) → mark(z0) 388.36/118.67
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.67
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.67
active(isNat(0)) → mark(tt) 388.36/118.67
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.67
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.67
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.67
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.67
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.67
active(U12(z0)) → U12(active(z0)) 388.36/118.67
active(U21(z0)) → U21(active(z0)) 388.36/118.67
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.67
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.67
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.67
active(s(z0)) → s(active(z0)) 388.36/118.67
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.67
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.67
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.67
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.67
U12(mark(z0)) → mark(U12(z0)) 388.36/118.67
U12(ok(z0)) → ok(U12(z0)) 388.36/118.67
U21(mark(z0)) → mark(U21(z0)) 388.36/118.67
U21(ok(z0)) → ok(U21(z0)) 388.36/118.67
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.67
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.67
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.67
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.67
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.67
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.67
s(mark(z0)) → mark(s(z0)) 388.36/118.67
s(ok(z0)) → ok(s(z0)) 388.36/118.67
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.67
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.67
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.67
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.67
proper(tt) → ok(tt) 388.36/118.67
proper(U12(z0)) → U12(proper(z0)) 388.36/118.67
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.67
proper(U21(z0)) → U21(proper(z0)) 388.36/118.67
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.67
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.67
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.67
proper(s(z0)) → s(proper(z0)) 388.36/118.67
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.67
proper(0) → ok(0) 388.36/118.67
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.67
top(mark(z0)) → top(proper(z0)) 388.36/118.67
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.67
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.67
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.67
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.67
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.67
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.67
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.67
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.67
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.67
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.67
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.67
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.67
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.67
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.67
S(mark(z0)) → c32(S(z0)) 388.36/118.67
S(ok(z0)) → c33(S(z0)) 388.36/118.67
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.67
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.67
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.67
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.67
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.67
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.67
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.67
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.67
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.67
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.67
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.67
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.67
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.67
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.67
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.67
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.67
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.67
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.67
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.67
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.67
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.67
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.67
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.67
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.67
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.67
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.67
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.67
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.67
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.67
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.67
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.67
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.67
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.67
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.67
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.67
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.67
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.67
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.67
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.67
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.67
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.67
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.67
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.67
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.67
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.67
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.67
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.67
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.67
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.67
PROPER(U12(tt)) → c39(U12'(ok(tt)), PROPER(tt)) 388.36/118.67
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.67
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.67
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.67
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.67
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.67
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.67
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.67
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.67
PROPER(U12(0)) → c39(U12'(ok(0)), PROPER(0))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.67
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.67
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.67
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.67
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.67
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.67
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.67
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.67
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.67
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.67
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.67
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.67
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.67
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.67
S(mark(z0)) → c32(S(z0)) 388.36/118.67
S(ok(z0)) → c33(S(z0)) 388.36/118.67
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.67
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.67
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.67
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.67
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.67
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.67
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.67
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.67
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.67
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.67
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.67
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.67
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.67
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.67
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.67
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.67
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.67
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.67
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.67
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.67
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.67
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.67
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.67
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.67
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.67
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.67
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.67
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.67
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.67
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.67
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.67
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.67
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.67
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.67
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.67
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.67
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.67
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.67
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.67
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.67
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.67
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.67
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.67
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.67
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.67
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.67
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.67
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.67
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.67
PROPER(U12(tt)) → c39(U12'(ok(tt)), PROPER(tt)) 388.36/118.67
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.67
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.67
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.67
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.67
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.67
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.67
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.67
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.67
PROPER(U12(0)) → c39(U12'(ok(0)), PROPER(0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39

388.36/118.67
388.36/118.67

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

Removed 2 trailing tuple parts
388.36/118.67
388.36/118.67

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.67
active(U12(tt)) → mark(tt) 388.36/118.67
active(U21(tt)) → mark(tt) 388.36/118.67
active(U31(tt, z0)) → mark(z0) 388.36/118.67
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.67
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.67
active(isNat(0)) → mark(tt) 388.36/118.67
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.67
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.67
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.67
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.67
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.67
active(U12(z0)) → U12(active(z0)) 388.36/118.67
active(U21(z0)) → U21(active(z0)) 388.36/118.67
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.67
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.67
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.67
active(s(z0)) → s(active(z0)) 388.36/118.67
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.67
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.67
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.67
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.67
U12(mark(z0)) → mark(U12(z0)) 388.36/118.67
U12(ok(z0)) → ok(U12(z0)) 388.36/118.67
U21(mark(z0)) → mark(U21(z0)) 388.36/118.67
U21(ok(z0)) → ok(U21(z0)) 388.36/118.67
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.67
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.67
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.67
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.67
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.67
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.67
s(mark(z0)) → mark(s(z0)) 388.36/118.67
s(ok(z0)) → ok(s(z0)) 388.36/118.67
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.67
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.67
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.67
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.67
proper(tt) → ok(tt) 388.36/118.67
proper(U12(z0)) → U12(proper(z0)) 388.36/118.67
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.67
proper(U21(z0)) → U21(proper(z0)) 388.36/118.67
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.67
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.67
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.67
proper(s(z0)) → s(proper(z0)) 388.36/118.67
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.67
proper(0) → ok(0) 388.36/118.67
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.67
top(mark(z0)) → top(proper(z0)) 388.36/118.67
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.67
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.67
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.67
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.67
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.67
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.67
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.67
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.67
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.67
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.67
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.67
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.67
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.67
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.67
S(mark(z0)) → c32(S(z0)) 388.36/118.67
S(ok(z0)) → c33(S(z0)) 388.36/118.67
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.67
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.67
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.67
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.67
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.67
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.67
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.67
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.67
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.67
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.67
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.67
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.67
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.67
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.67
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.67
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.67
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.67
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.67
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.67
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.67
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.67
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.67
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.67
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.67
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.67
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.67
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.67
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.67
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.67
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.67
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.67
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.67
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.67
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.67
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.67
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.67
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.67
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.67
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.67
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.67
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.67
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.67
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.67
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.67
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.67
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.67
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.67
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.67
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.67
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.67
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.67
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.67
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.67
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.67
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.67
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.67
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.67
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.36/118.67
PROPER(U12(0)) → c39(U12'(ok(0)))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.67
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.67
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.67
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.67
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.67
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.67
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.67
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.67
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.67
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.67
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.67
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.67
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.67
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.67
S(mark(z0)) → c32(S(z0)) 388.36/118.67
S(ok(z0)) → c33(S(z0)) 388.36/118.67
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.67
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.67
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.67
PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.67
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.67
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.67
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.67
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.67
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.67
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.67
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.67
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.67
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.67
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.67
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.67
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.67
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.67
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.67
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.67
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.67
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.67
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.67
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.67
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.67
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.67
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.67
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.67
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.67
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.67
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.67
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.67
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.67
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.67
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.67
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.67
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.67
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.67
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.67
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.67
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.67
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.67
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.67
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.67
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.67
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.67
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.67
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.67
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.67
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.67
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.67
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.67
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.67
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.67
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.67
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.67
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.67
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.67
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.67
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.67
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.67
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.67
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.67
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.67
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.67
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.67
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.67
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.67
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.67
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.67
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.67
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.67
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.67
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.67
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.67
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.67
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.67
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.67
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.67
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.67
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.67
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.67
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.67
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.67
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.67
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.67
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.67
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.67
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.67
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.67
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.67
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.36/118.67
PROPER(U12(0)) → c39(U12'(ok(0)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c40, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39

388.36/118.67
388.36/118.67

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

Use narrowing to replace PROPER(isNat(z0)) → c40(ISNAT(proper(z0)), PROPER(z0)) by

PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.67
PROPER(isNat(tt)) → c40(ISNAT(ok(tt)), PROPER(tt)) 388.36/118.67
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.67
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.67
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.67
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.67
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.67
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.67
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.36/118.67
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.67
PROPER(isNat(0)) → c40(ISNAT(ok(0)), PROPER(0))
388.36/118.67
388.36/118.67

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.67
active(U12(tt)) → mark(tt) 388.36/118.67
active(U21(tt)) → mark(tt) 388.36/118.67
active(U31(tt, z0)) → mark(z0) 388.36/118.67
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.67
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.67
active(isNat(0)) → mark(tt) 388.36/118.67
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.67
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.67
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.67
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.67
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.67
active(U12(z0)) → U12(active(z0)) 388.36/118.67
active(U21(z0)) → U21(active(z0)) 388.36/118.67
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.67
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.67
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.67
active(s(z0)) → s(active(z0)) 388.36/118.67
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.67
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.67
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.67
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.67
U12(mark(z0)) → mark(U12(z0)) 388.36/118.67
U12(ok(z0)) → ok(U12(z0)) 388.36/118.67
U21(mark(z0)) → mark(U21(z0)) 388.36/118.67
U21(ok(z0)) → ok(U21(z0)) 388.36/118.67
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.67
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.67
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.67
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.67
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.67
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.67
s(mark(z0)) → mark(s(z0)) 388.36/118.67
s(ok(z0)) → ok(s(z0)) 388.36/118.67
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.67
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.67
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.67
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.67
proper(tt) → ok(tt) 388.36/118.67
proper(U12(z0)) → U12(proper(z0)) 388.36/118.67
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.67
proper(U21(z0)) → U21(proper(z0)) 388.36/118.67
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.67
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.67
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.67
proper(s(z0)) → s(proper(z0)) 388.36/118.67
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.67
proper(0) → ok(0) 388.36/118.67
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.67
top(mark(z0)) → top(proper(z0)) 388.36/118.67
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.67
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.67
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.67
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.67
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.67
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.67
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.67
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.67
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.67
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.67
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.67
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.68
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.68
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.68
S(mark(z0)) → c32(S(z0)) 388.36/118.68
S(ok(z0)) → c33(S(z0)) 388.36/118.68
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.68
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.68
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.68
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.68
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.68
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.68
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.68
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.68
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.68
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.68
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.68
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.68
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.68
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.68
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.68
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.68
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.68
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.68
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.68
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.68
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.68
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.68
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.68
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.68
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.68
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.68
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.68
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.68
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.68
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.68
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.68
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.68
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.68
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.68
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.68
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.68
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.68
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.68
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.68
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.68
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.68
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.68
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.68
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.68
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.68
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.68
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.68
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.68
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.68
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.36/118.68
PROPER(U12(0)) → c39(U12'(ok(0))) 388.36/118.68
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(isNat(tt)) → c40(ISNAT(ok(tt)), PROPER(tt)) 388.36/118.68
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.68
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.68
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.68
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.36/118.68
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(isNat(0)) → c40(ISNAT(ok(0)), PROPER(0))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.68
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.68
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.68
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.68
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.68
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.68
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.68
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.68
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.68
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.68
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.68
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.68
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.68
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.68
S(mark(z0)) → c32(S(z0)) 388.36/118.68
S(ok(z0)) → c33(S(z0)) 388.36/118.68
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.68
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.68
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.68
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.68
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.68
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.68
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.68
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.68
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.68
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.68
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.68
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.68
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.68
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.68
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.68
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.68
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.68
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.68
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.68
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.68
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.68
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.68
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.68
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.68
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.68
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.68
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.68
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.68
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.68
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.68
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.68
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.68
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.68
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.68
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.68
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.68
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.68
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.68
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.68
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.68
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.68
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.68
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.68
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.68
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.68
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.68
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.68
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.68
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.68
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.36/118.68
PROPER(U12(0)) → c39(U12'(ok(0))) 388.36/118.68
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(isNat(tt)) → c40(ISNAT(ok(tt)), PROPER(tt)) 388.36/118.68
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.68
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.68
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.68
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.36/118.68
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(isNat(0)) → c40(ISNAT(ok(0)), PROPER(0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40

388.36/118.68
388.36/118.68

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

Removed 2 trailing tuple parts
388.36/118.68
388.36/118.68

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.68
active(U12(tt)) → mark(tt) 388.36/118.68
active(U21(tt)) → mark(tt) 388.36/118.68
active(U31(tt, z0)) → mark(z0) 388.36/118.68
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.68
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.68
active(isNat(0)) → mark(tt) 388.36/118.68
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.68
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.68
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.68
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.68
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.68
active(U12(z0)) → U12(active(z0)) 388.36/118.68
active(U21(z0)) → U21(active(z0)) 388.36/118.68
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.68
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.68
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.68
active(s(z0)) → s(active(z0)) 388.36/118.68
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.68
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.68
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.68
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.68
U12(mark(z0)) → mark(U12(z0)) 388.36/118.68
U12(ok(z0)) → ok(U12(z0)) 388.36/118.68
U21(mark(z0)) → mark(U21(z0)) 388.36/118.68
U21(ok(z0)) → ok(U21(z0)) 388.36/118.68
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.68
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.68
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.68
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.68
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.68
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.68
s(mark(z0)) → mark(s(z0)) 388.36/118.68
s(ok(z0)) → ok(s(z0)) 388.36/118.68
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.68
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.68
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.68
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.68
proper(tt) → ok(tt) 388.36/118.68
proper(U12(z0)) → U12(proper(z0)) 388.36/118.68
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.68
proper(U21(z0)) → U21(proper(z0)) 388.36/118.68
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.68
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.68
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.68
proper(s(z0)) → s(proper(z0)) 388.36/118.68
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.68
proper(0) → ok(0) 388.36/118.68
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.68
top(mark(z0)) → top(proper(z0)) 388.36/118.68
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.68
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.68
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.68
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.68
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.68
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.68
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.68
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.68
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.68
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.68
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.68
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.68
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.68
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.68
S(mark(z0)) → c32(S(z0)) 388.36/118.68
S(ok(z0)) → c33(S(z0)) 388.36/118.68
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.68
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.68
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.68
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.68
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.68
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.68
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.68
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.68
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.68
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.68
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.68
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.68
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.68
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.68
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.68
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.68
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.68
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.68
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.68
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.68
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.68
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.68
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.68
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.68
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.68
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.68
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.68
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.68
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.68
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.68
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.68
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.68
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.68
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.68
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.68
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.68
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.68
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.68
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.68
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.68
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.68
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.68
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.68
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.68
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.68
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.68
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.68
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.68
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.68
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.36/118.68
PROPER(U12(0)) → c39(U12'(ok(0))) 388.36/118.68
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.68
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.68
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.68
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.36/118.68
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.36/118.68
PROPER(isNat(0)) → c40(ISNAT(ok(0)))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.68
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.68
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.68
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.68
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.68
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.68
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.68
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.68
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.68
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.68
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.68
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.68
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.68
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.68
S(mark(z0)) → c32(S(z0)) 388.36/118.68
S(ok(z0)) → c33(S(z0)) 388.36/118.68
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.68
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.68
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.68
PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) 388.36/118.68
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.68
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.68
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.68
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.68
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.68
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.68
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.68
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.68
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.68
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.68
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.68
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.68
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.68
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.68
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.68
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.68
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.68
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.68
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.68
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.68
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.68
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.68
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.68
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.68
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.68
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.68
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.68
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.68
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.68
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.68
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.68
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.68
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.68
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.68
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.68
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.68
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.68
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.68
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.68
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.68
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.68
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.68
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.68
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.68
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.68
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.68
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.68
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.68
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.68
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.68
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.68
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.68
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.68
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.68
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.68
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.68
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.36/118.68
PROPER(U12(0)) → c39(U12'(ok(0))) 388.36/118.68
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.68
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.68
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.68
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.36/118.68
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.36/118.68
PROPER(isNat(0)) → c40(ISNAT(ok(0)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c41, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40

388.36/118.68
388.36/118.68

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

Use narrowing to replace PROPER(U21(z0)) → c41(U21'(proper(z0)), PROPER(z0)) by

PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.68
PROPER(U21(tt)) → c41(U21'(ok(tt)), PROPER(tt)) 388.36/118.68
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.68
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.68
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.68
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.68
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.68
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.68
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.36/118.68
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.68
PROPER(U21(0)) → c41(U21'(ok(0)), PROPER(0))
388.36/118.68
388.36/118.68

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.68
active(U12(tt)) → mark(tt) 388.36/118.68
active(U21(tt)) → mark(tt) 388.36/118.68
active(U31(tt, z0)) → mark(z0) 388.36/118.68
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.68
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.68
active(isNat(0)) → mark(tt) 388.36/118.68
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.68
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.68
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.68
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.68
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.68
active(U12(z0)) → U12(active(z0)) 388.36/118.68
active(U21(z0)) → U21(active(z0)) 388.36/118.68
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.68
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.68
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.68
active(s(z0)) → s(active(z0)) 388.36/118.68
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.68
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.68
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.68
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.68
U12(mark(z0)) → mark(U12(z0)) 388.36/118.68
U12(ok(z0)) → ok(U12(z0)) 388.36/118.68
U21(mark(z0)) → mark(U21(z0)) 388.36/118.68
U21(ok(z0)) → ok(U21(z0)) 388.36/118.68
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.68
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.68
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.68
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.68
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.68
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.68
s(mark(z0)) → mark(s(z0)) 388.36/118.68
s(ok(z0)) → ok(s(z0)) 388.36/118.68
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.68
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.68
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.68
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.68
proper(tt) → ok(tt) 388.36/118.68
proper(U12(z0)) → U12(proper(z0)) 388.36/118.68
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.68
proper(U21(z0)) → U21(proper(z0)) 388.36/118.68
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.68
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.68
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.68
proper(s(z0)) → s(proper(z0)) 388.36/118.68
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.68
proper(0) → ok(0) 388.36/118.68
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.68
top(mark(z0)) → top(proper(z0)) 388.36/118.68
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.68
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.68
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.68
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.68
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.68
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.68
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.68
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.68
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.68
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.68
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.68
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.68
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.68
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.68
S(mark(z0)) → c32(S(z0)) 388.36/118.68
S(ok(z0)) → c33(S(z0)) 388.36/118.68
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.68
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.68
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.68
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.68
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.68
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.68
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.68
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.68
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.68
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.68
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.68
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.68
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.68
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.68
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.68
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.68
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.68
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.68
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.68
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.68
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.68
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.68
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.68
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.68
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.68
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.68
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.68
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.68
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.68
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.68
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.68
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.68
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.68
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.68
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.68
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.68
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.68
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.68
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.68
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.68
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.68
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.68
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.69
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.69
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.69
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.69
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.69
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.69
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.69
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.69
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.69
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.69
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.69
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.69
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.69
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.69
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.69
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.69
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.69
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.69
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.69
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.69
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.69
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.69
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.69
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.69
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.69
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.69
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.36/118.69
PROPER(U12(0)) → c39(U12'(ok(0))) 388.36/118.69
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.36/118.69
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.36/118.69
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U21(tt)) → c41(U21'(ok(tt)), PROPER(tt)) 388.36/118.69
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U21(0)) → c41(U21'(ok(0)), PROPER(0))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.69
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.69
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.69
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.69
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.69
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.69
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.69
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.69
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.69
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.69
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.69
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.69
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.69
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.69
S(mark(z0)) → c32(S(z0)) 388.36/118.69
S(ok(z0)) → c33(S(z0)) 388.36/118.69
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.69
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.69
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.69
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.69
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.69
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.69
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.69
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.69
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.69
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.69
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.69
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.69
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.69
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.69
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.69
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.69
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.69
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.69
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.69
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.69
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.69
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.69
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.69
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.69
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.69
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.69
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.69
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.69
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.69
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.69
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.69
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.69
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.69
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.69
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.69
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.69
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.69
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.69
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.69
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.69
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.69
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.69
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.69
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.69
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.69
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.69
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.69
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.69
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.69
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.69
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.69
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.69
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.69
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.69
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.69
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.69
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.69
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.69
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.69
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.69
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.69
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.69
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.69
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.69
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.69
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.36/118.69
PROPER(U12(0)) → c39(U12'(ok(0))) 388.36/118.69
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.36/118.69
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.36/118.69
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U21(tt)) → c41(U21'(ok(tt)), PROPER(tt)) 388.36/118.69
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U21(0)) → c41(U21'(ok(0)), PROPER(0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41

388.36/118.69
388.36/118.69

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

Removed 2 trailing tuple parts
388.36/118.69
388.36/118.69

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.69
active(U12(tt)) → mark(tt) 388.36/118.69
active(U21(tt)) → mark(tt) 388.36/118.69
active(U31(tt, z0)) → mark(z0) 388.36/118.69
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.69
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.69
active(isNat(0)) → mark(tt) 388.36/118.69
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.69
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.69
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.69
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.69
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.69
active(U12(z0)) → U12(active(z0)) 388.36/118.69
active(U21(z0)) → U21(active(z0)) 388.36/118.69
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.69
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.69
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.69
active(s(z0)) → s(active(z0)) 388.36/118.69
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.69
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.69
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.69
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.69
U12(mark(z0)) → mark(U12(z0)) 388.36/118.69
U12(ok(z0)) → ok(U12(z0)) 388.36/118.69
U21(mark(z0)) → mark(U21(z0)) 388.36/118.69
U21(ok(z0)) → ok(U21(z0)) 388.36/118.69
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.69
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.69
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.69
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.69
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.69
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.69
s(mark(z0)) → mark(s(z0)) 388.36/118.69
s(ok(z0)) → ok(s(z0)) 388.36/118.69
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.69
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.69
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.69
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.69
proper(tt) → ok(tt) 388.36/118.69
proper(U12(z0)) → U12(proper(z0)) 388.36/118.69
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.69
proper(U21(z0)) → U21(proper(z0)) 388.36/118.69
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.69
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.69
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.69
proper(s(z0)) → s(proper(z0)) 388.36/118.69
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.69
proper(0) → ok(0) 388.36/118.69
isNat(ok(z0)) → ok(isNat(z0)) 388.36/118.69
top(mark(z0)) → top(proper(z0)) 388.36/118.69
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.69
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.69
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.69
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.69
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.69
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.69
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.69
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.69
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.69
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.69
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.69
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.69
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.69
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.69
S(mark(z0)) → c32(S(z0)) 388.36/118.69
S(ok(z0)) → c33(S(z0)) 388.36/118.69
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.69
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.69
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.69
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.69
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.69
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.69
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.69
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.69
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.69
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.69
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.69
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.69
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.69
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.69
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.69
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.69
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.69
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.69
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.69
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.69
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.69
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.69
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.69
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.69
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.69
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.69
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.69
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.69
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.69
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.69
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.69
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.69
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.69
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.69
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.69
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.69
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.69
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.69
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.69
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.69
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.69
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.69
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.69
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.69
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.69
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.69
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.69
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.69
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.69
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.69
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.69
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.69
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.69
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.69
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.69
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.69
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.69
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.69
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.69
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.69
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.69
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.69
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.69
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.69
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.69
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.36/118.69
PROPER(U12(0)) → c39(U12'(ok(0))) 388.36/118.69
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.36/118.69
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.36/118.69
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.36/118.69
PROPER(U21(0)) → c41(U21'(ok(0)))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.36/118.69
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.36/118.69
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.36/118.69
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.36/118.69
U12'(mark(z0)) → c22(U12'(z0)) 388.36/118.69
U12'(ok(z0)) → c23(U12'(z0)) 388.36/118.69
U21'(mark(z0)) → c24(U21'(z0)) 388.36/118.69
U21'(ok(z0)) → c25(U21'(z0)) 388.36/118.69
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.36/118.69
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.36/118.69
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.36/118.69
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.36/118.69
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.36/118.69
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.36/118.69
S(mark(z0)) → c32(S(z0)) 388.36/118.69
S(ok(z0)) → c33(S(z0)) 388.36/118.69
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.36/118.69
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.36/118.69
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.36/118.69
PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.69
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.69
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.36/118.69
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.36/118.69
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.36/118.69
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.36/118.69
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.36/118.69
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.36/118.69
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.36/118.69
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.36/118.69
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.36/118.69
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.36/118.69
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.36/118.69
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.36/118.69
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.36/118.69
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.36/118.69
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.36/118.69
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.36/118.69
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.36/118.69
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.36/118.69
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.69
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.69
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.69
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.36/118.69
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.36/118.69
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.36/118.69
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.36/118.69
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.36/118.69
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.36/118.69
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.36/118.69
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.36/118.69
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.36/118.69
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.36/118.69
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.36/118.69
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.36/118.69
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.36/118.69
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.36/118.69
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.36/118.69
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.36/118.69
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.36/118.69
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.36/118.69
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.36/118.69
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.36/118.69
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.69
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.36/118.69
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.69
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.36/118.69
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.36/118.69
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.36/118.69
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.69
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.36/118.69
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.36/118.69
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.36/118.69
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.36/118.69
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.36/118.69
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.36/118.69
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.36/118.69
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.36/118.69
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.36/118.69
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.36/118.69
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.36/118.69
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.36/118.69
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.36/118.69
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.36/118.69
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.36/118.69
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.36/118.69
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.36/118.69
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.36/118.69
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.36/118.69
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.36/118.69
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.36/118.69
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.36/118.69
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.36/118.69
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.36/118.69
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.36/118.69
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.69
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.69
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.69
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.69
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.69
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.69
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.69
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.36/118.69
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.36/118.69
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.36/118.69
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.36/118.69
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.36/118.69
PROPER(U12(0)) → c39(U12'(ok(0))) 388.36/118.69
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.36/118.69
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.36/118.69
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.36/118.69
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.36/118.69
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.36/118.69
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.36/118.69
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.36/118.69
PROPER(U21(0)) → c41(U21'(ok(0)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c42, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41

388.36/118.69
388.36/118.69

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

Use narrowing to replace PROPER(U31(z0, z1)) → c42(U31'(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.36/118.69
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 388.36/118.69
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.36/118.69
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.36/118.69
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.36/118.69
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.36/118.69
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.36/118.69
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.36/118.69
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.36/118.69
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.36/118.69
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 388.36/118.69
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 388.36/118.69
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.36/118.69
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.36/118.69
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.36/118.69
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.36/118.69
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.36/118.69
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.36/118.69
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.36/118.69
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
388.36/118.69
388.36/118.69

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.36/118.69
active(U12(tt)) → mark(tt) 388.36/118.69
active(U21(tt)) → mark(tt) 388.36/118.69
active(U31(tt, z0)) → mark(z0) 388.36/118.69
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.36/118.69
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.36/118.69
active(isNat(0)) → mark(tt) 388.36/118.69
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.36/118.69
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.36/118.69
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.36/118.69
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.36/118.69
active(U11(z0, z1)) → U11(active(z0), z1) 388.36/118.69
active(U12(z0)) → U12(active(z0)) 388.36/118.69
active(U21(z0)) → U21(active(z0)) 388.36/118.69
active(U31(z0, z1)) → U31(active(z0), z1) 388.36/118.69
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.36/118.69
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.36/118.69
active(s(z0)) → s(active(z0)) 388.36/118.69
active(plus(z0, z1)) → plus(active(z0), z1) 388.36/118.69
active(plus(z0, z1)) → plus(z0, active(z1)) 388.36/118.69
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.36/118.69
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.36/118.69
U12(mark(z0)) → mark(U12(z0)) 388.36/118.69
U12(ok(z0)) → ok(U12(z0)) 388.36/118.69
U21(mark(z0)) → mark(U21(z0)) 388.36/118.69
U21(ok(z0)) → ok(U21(z0)) 388.36/118.69
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.36/118.69
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.36/118.69
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.36/118.69
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.36/118.69
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.36/118.69
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.36/118.69
s(mark(z0)) → mark(s(z0)) 388.36/118.69
s(ok(z0)) → ok(s(z0)) 388.36/118.69
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.36/118.69
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.36/118.69
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.36/118.69
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.36/118.69
proper(tt) → ok(tt) 388.36/118.69
proper(U12(z0)) → U12(proper(z0)) 388.36/118.69
proper(isNat(z0)) → isNat(proper(z0)) 388.36/118.69
proper(U21(z0)) → U21(proper(z0)) 388.36/118.69
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.36/118.69
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.36/118.69
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.36/118.69
proper(s(z0)) → s(proper(z0)) 388.36/118.69
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.36/118.69
proper(0) → ok(0) 388.36/118.69
isNat(ok(z0)) → ok(isNat(z0)) 388.73/118.73
top(mark(z0)) → top(proper(z0)) 388.73/118.73
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.73
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.73
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.73
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.73
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.73
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.73
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.73
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.73
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.73
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.73
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.73
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.73
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.73
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.73
S(mark(z0)) → c32(S(z0)) 388.73/118.73
S(ok(z0)) → c33(S(z0)) 388.73/118.73
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.73
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.73
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.73
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.73
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.73
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.73
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.73
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.73
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.73
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.73
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.73
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.73
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.73
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.73
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.73
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.73
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.73
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.73
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.73
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.73
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.73
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.73
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.73
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.73
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.73
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.73
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.73
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.73
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.73
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.73
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.73
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.73
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.73
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.73
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.73
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.73
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.73
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.73
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.73
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.73
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.73
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.73
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.73
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.73
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.73
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.73
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.73
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.73
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.73
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.73
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.73
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.73
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.73
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.73
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.73
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.73
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.73
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.73
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.73
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 388.73/118.73
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.73
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.73
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.73
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.73
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 388.73/118.73
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 388.73/118.73
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.73
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.73
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.73
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.73
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.73
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.73
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.73
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.73
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.73
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.73
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.73
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.73
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.73
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.73
S(mark(z0)) → c32(S(z0)) 388.73/118.73
S(ok(z0)) → c33(S(z0)) 388.73/118.73
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.73
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.73
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.73
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.73
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.73
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.73
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.73
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.73
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.73
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.73
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.73
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.73
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.73
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.73
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.73
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.73
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.73
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.73
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.73
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.73
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.73
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.73
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.73
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.73
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.73
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.73
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.73
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.73
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.73
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.73
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.73
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.73
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.73
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.73
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.73
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.73
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.73
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.73
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.73
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.73
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.73
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.73
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.73
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.73
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.73
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.73
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.73
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.73
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.73
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.73
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.73
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.73
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.73
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.73
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.73
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.73
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.73
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.73
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.73
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 388.73/118.73
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.73
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.73
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.73
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.73
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 388.73/118.73
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 388.73/118.73
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(0), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42

388.73/118.73
388.73/118.73

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

Removed 4 trailing tuple parts
388.73/118.73
388.73/118.73

(68) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.73/118.73
active(U12(tt)) → mark(tt) 388.73/118.73
active(U21(tt)) → mark(tt) 388.73/118.73
active(U31(tt, z0)) → mark(z0) 388.73/118.73
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.73/118.73
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.73/118.73
active(isNat(0)) → mark(tt) 388.73/118.73
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.73/118.73
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.73/118.73
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.73/118.73
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.73/118.73
active(U11(z0, z1)) → U11(active(z0), z1) 388.73/118.73
active(U12(z0)) → U12(active(z0)) 388.73/118.73
active(U21(z0)) → U21(active(z0)) 388.73/118.73
active(U31(z0, z1)) → U31(active(z0), z1) 388.73/118.73
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.73/118.73
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.73/118.73
active(s(z0)) → s(active(z0)) 388.73/118.73
active(plus(z0, z1)) → plus(active(z0), z1) 388.73/118.73
active(plus(z0, z1)) → plus(z0, active(z1)) 388.73/118.73
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.73/118.73
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.73/118.73
U12(mark(z0)) → mark(U12(z0)) 388.73/118.73
U12(ok(z0)) → ok(U12(z0)) 388.73/118.73
U21(mark(z0)) → mark(U21(z0)) 388.73/118.73
U21(ok(z0)) → ok(U21(z0)) 388.73/118.73
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.73/118.73
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.73/118.73
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.73/118.73
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.73/118.73
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.73/118.73
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.73/118.73
s(mark(z0)) → mark(s(z0)) 388.73/118.73
s(ok(z0)) → ok(s(z0)) 388.73/118.73
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.73/118.73
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.73/118.73
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.73/118.73
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.73/118.73
proper(tt) → ok(tt) 388.73/118.73
proper(U12(z0)) → U12(proper(z0)) 388.73/118.73
proper(isNat(z0)) → isNat(proper(z0)) 388.73/118.73
proper(U21(z0)) → U21(proper(z0)) 388.73/118.73
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.73/118.73
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.73/118.73
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.73/118.73
proper(s(z0)) → s(proper(z0)) 388.73/118.73
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.73/118.73
proper(0) → ok(0) 388.73/118.73
isNat(ok(z0)) → ok(isNat(z0)) 388.73/118.73
top(mark(z0)) → top(proper(z0)) 388.73/118.73
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.73
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.73
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.73
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.73
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.73
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.73
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.73
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.73
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.73
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.73
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.73
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.73
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.73
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.73
S(mark(z0)) → c32(S(z0)) 388.73/118.73
S(ok(z0)) → c33(S(z0)) 388.73/118.73
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.73
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.73
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.73
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.73
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.73
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.73
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.73
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.73
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.73
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.73
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.73
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.73
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.73
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.73
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.73
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.73
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.73
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.73
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.73
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.73
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.73
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.73
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.73
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.73
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.73
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.73
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.73
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.73
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.73
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.73
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.73
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.73
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.73
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.73
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.73
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.73
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.73
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.73
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.73
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.73
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.73
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.73
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.73
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.73
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.73
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.73
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.73
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.73
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.73
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.73
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.73
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.73
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.73
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.73
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.73
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.73
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.73
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.73
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.73
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.73
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.73
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.73
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.73
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.73
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.73
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.73
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.73
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.73
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.73
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.73
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.73
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.73
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.73
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.73
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.73
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.73
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.73
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.73
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.73
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.73
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.73
S(mark(z0)) → c32(S(z0)) 388.73/118.73
S(ok(z0)) → c33(S(z0)) 388.73/118.73
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.73
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.73
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.73
PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.73
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.73
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.73
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.73
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.73
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.73
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.73
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.73
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.73
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.73
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.73
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.73
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.73
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.73
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.73
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.73
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.73
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.73
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.73
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.73
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.73
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.73
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.73
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.73
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.73
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.73
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.73
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.73
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.73
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.73
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.73
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.73
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.73
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.73
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.73
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.73
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.73
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.73
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.73
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.73
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.73
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.73
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.73
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.73
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.73
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.73
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.73
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.73
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.73
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.73
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.73
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.73
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.73
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.73
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.73
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.73
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.73
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.73
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.73
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.73
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.73
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.73
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.73
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.73
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.73
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.73
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.73
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.73
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.73
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.73
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.73
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.73
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.73
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.73
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.73
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.73
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.73
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.73
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.73
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.74
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.74
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.74
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.74
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.74
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.74
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.74
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.74
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.74
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.74
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.74
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.74
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.74
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.74
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.74
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.74
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.74
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.74
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.74
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.74
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.74
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.74
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.74
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.74
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.74
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.74
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.74
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.74
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.74
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.74
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.74
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.74
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.74
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.74
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.74
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.74
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.74
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.74
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.74
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.74
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.74
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.74
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.74
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.74
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.74
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.74
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.74
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.74
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.74
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c43, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42

388.73/118.74
388.73/118.74

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

Use narrowing to replace PROPER(U41(z0, z1, z2)) → c43(U41'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) by

PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.74
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 388.73/118.74
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.74
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.74
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.74
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.74
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.74
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.74
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.74
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.74
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 388.73/118.74
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.74
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 388.73/118.74
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.74
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.74
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.74
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.74
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.74
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.74
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.74
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.74
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 388.73/118.74
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.74
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 388.73/118.74
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.74
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.74
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.74
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.74
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.74
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.74
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.74
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.74
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
388.73/118.74
388.73/118.74

(70) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.73/118.74
active(U12(tt)) → mark(tt) 388.73/118.74
active(U21(tt)) → mark(tt) 388.73/118.74
active(U31(tt, z0)) → mark(z0) 388.73/118.74
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.73/118.74
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.73/118.74
active(isNat(0)) → mark(tt) 388.73/118.74
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.73/118.74
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.73/118.74
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.73/118.74
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.73/118.74
active(U11(z0, z1)) → U11(active(z0), z1) 388.73/118.74
active(U12(z0)) → U12(active(z0)) 388.73/118.74
active(U21(z0)) → U21(active(z0)) 388.73/118.74
active(U31(z0, z1)) → U31(active(z0), z1) 388.73/118.74
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.73/118.74
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.73/118.74
active(s(z0)) → s(active(z0)) 388.73/118.74
active(plus(z0, z1)) → plus(active(z0), z1) 388.73/118.74
active(plus(z0, z1)) → plus(z0, active(z1)) 388.73/118.74
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.73/118.74
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.73/118.74
U12(mark(z0)) → mark(U12(z0)) 388.73/118.74
U12(ok(z0)) → ok(U12(z0)) 388.73/118.74
U21(mark(z0)) → mark(U21(z0)) 388.73/118.74
U21(ok(z0)) → ok(U21(z0)) 388.73/118.74
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.73/118.74
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.73/118.74
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.73/118.74
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.73/118.74
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.73/118.74
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.73/118.74
s(mark(z0)) → mark(s(z0)) 388.73/118.74
s(ok(z0)) → ok(s(z0)) 388.73/118.74
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.73/118.74
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.73/118.74
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.73/118.74
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.73/118.74
proper(tt) → ok(tt) 388.73/118.74
proper(U12(z0)) → U12(proper(z0)) 388.73/118.74
proper(isNat(z0)) → isNat(proper(z0)) 388.73/118.74
proper(U21(z0)) → U21(proper(z0)) 388.73/118.74
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.73/118.74
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.73/118.74
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.73/118.74
proper(s(z0)) → s(proper(z0)) 388.73/118.74
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.73/118.74
proper(0) → ok(0) 388.73/118.74
isNat(ok(z0)) → ok(isNat(z0)) 388.73/118.74
top(mark(z0)) → top(proper(z0)) 388.73/118.74
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.74
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.74
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.74
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.74
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.74
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.74
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.74
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.74
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.74
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.74
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.74
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.74
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.74
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.74
S(mark(z0)) → c32(S(z0)) 388.73/118.74
S(ok(z0)) → c33(S(z0)) 388.73/118.74
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.74
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.74
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.74
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.74
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.74
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.74
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.74
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.74
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.74
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.74
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.74
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.74
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.74
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.74
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.74
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.74
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.74
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.74
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.74
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.74
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.74
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.74
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.74
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.74
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.74
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.74
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.74
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.74
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.74
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.75
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.75
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.75
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.75
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.75
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.75
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.75
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.75
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.75
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.75
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.75
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.75
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.75
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.75
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.75
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.75
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.75
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.75
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.75
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.75
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.75
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.75
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.75
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.75
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.75
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.75
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.75
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.75
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.75
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.75
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.75
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.75
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.75
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.75
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.75
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.75
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.75
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.75
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.75
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.75
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.75
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.75
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.75
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.75
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.75
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.75
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.75
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.75
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.75
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.75
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.75
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.75
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.75
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.75
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.75
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.75
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.75
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.75
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.75
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.75
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.75
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.75
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.75
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.75
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.75
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.75
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.75
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.75
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.75
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.75
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.75
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.75
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.75
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.75
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.75
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.75
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.75
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.75
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.75
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.75
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 388.73/118.75
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.75
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.75
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.75
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.75
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 388.73/118.75
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 388.73/118.75
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.75
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.75
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.75
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.75
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.75
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.75
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.75
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.75
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.75
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.75
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.75
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.75
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.75
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.75
S(mark(z0)) → c32(S(z0)) 388.73/118.75
S(ok(z0)) → c33(S(z0)) 388.73/118.75
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.75
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.75
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.75
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.75
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.75
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.75
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.75
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.75
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.75
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.75
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.75
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.75
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.75
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.75
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.75
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.75
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.75
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.75
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.75
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.75
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.75
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.75
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.75
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.75
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.75
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.75
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.75
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.75
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.75
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.75
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.75
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.75
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.75
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.75
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.75
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.75
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.75
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.75
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.75
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.75
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.75
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.75
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.75
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.75
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.75
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.75
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.75
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.75
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.75
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.75
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.75
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.75
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.75
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.75
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.75
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.75
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.75
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.75
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.75
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.75
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.75
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.75
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.75
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.75
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.75
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.75
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.75
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.75
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.75
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.75
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.75
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.75
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.75
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.75
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.75
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.75
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.75
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.75
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.75
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.75
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.75
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.75
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.75
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.75
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.75
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.75
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.75
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.75
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.75
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.75
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.75
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.75
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.75
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.75
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.75
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.75
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.75
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.75
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.75
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.75
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.75
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 388.73/118.75
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.75
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.75
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.75
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.75
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 388.73/118.75
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 388.73/118.75
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.75
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42, c43

388.73/118.75
388.73/118.75

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

Removed 6 trailing tuple parts
388.73/118.75
388.73/118.75

(72) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.73/118.75
active(U12(tt)) → mark(tt) 388.73/118.75
active(U21(tt)) → mark(tt) 388.73/118.75
active(U31(tt, z0)) → mark(z0) 388.73/118.75
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.73/118.75
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.73/118.75
active(isNat(0)) → mark(tt) 388.73/118.75
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.73/118.75
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.73/118.75
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.73/118.75
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.73/118.75
active(U11(z0, z1)) → U11(active(z0), z1) 388.73/118.75
active(U12(z0)) → U12(active(z0)) 388.73/118.75
active(U21(z0)) → U21(active(z0)) 388.73/118.75
active(U31(z0, z1)) → U31(active(z0), z1) 388.73/118.75
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.73/118.75
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.73/118.75
active(s(z0)) → s(active(z0)) 388.73/118.75
active(plus(z0, z1)) → plus(active(z0), z1) 388.73/118.75
active(plus(z0, z1)) → plus(z0, active(z1)) 388.73/118.75
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.73/118.75
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.73/118.75
U12(mark(z0)) → mark(U12(z0)) 388.73/118.75
U12(ok(z0)) → ok(U12(z0)) 388.73/118.75
U21(mark(z0)) → mark(U21(z0)) 388.73/118.75
U21(ok(z0)) → ok(U21(z0)) 388.73/118.75
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.73/118.75
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.73/118.75
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.73/118.75
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.73/118.75
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.73/118.75
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.73/118.75
s(mark(z0)) → mark(s(z0)) 388.73/118.75
s(ok(z0)) → ok(s(z0)) 388.73/118.75
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.73/118.75
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.73/118.75
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.73/118.75
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.73/118.75
proper(tt) → ok(tt) 388.73/118.75
proper(U12(z0)) → U12(proper(z0)) 388.73/118.75
proper(isNat(z0)) → isNat(proper(z0)) 388.73/118.75
proper(U21(z0)) → U21(proper(z0)) 388.73/118.75
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.73/118.75
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.73/118.75
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.73/118.75
proper(s(z0)) → s(proper(z0)) 388.73/118.75
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.73/118.75
proper(0) → ok(0) 388.73/118.75
isNat(ok(z0)) → ok(isNat(z0)) 388.73/118.75
top(mark(z0)) → top(proper(z0)) 388.73/118.75
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.75
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.75
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.75
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.75
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.75
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.75
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.75
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.75
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.75
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.75
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.75
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.75
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.75
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.75
S(mark(z0)) → c32(S(z0)) 388.73/118.75
S(ok(z0)) → c33(S(z0)) 388.73/118.75
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.75
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.75
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.75
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.75
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.75
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.75
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.75
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.75
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.75
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.75
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.75
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.75
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.75
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.75
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.75
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.75
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.75
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.75
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.75
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.75
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.75
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.75
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.75
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.75
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.75
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.75
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.75
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.75
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.75
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.75
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.75
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.75
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.75
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.75
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.75
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.75
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.75
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.75
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.75
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.75
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.75
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.75
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.75
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.75
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.75
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.75
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.75
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.75
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.75
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.75
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.75
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.75
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.75
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.75
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.75
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.75
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.75
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.75
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.75
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.75
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.75
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.75
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.75
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.75
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.75
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.75
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.75
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.75
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.75
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.75
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.75
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.75
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.75
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.75
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.75
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.75
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.75
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.75
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.75
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.75
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.75
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.75
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.75
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.75
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.75
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.75
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.75
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.75
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.75
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.75
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.75
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.75
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.75
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.75
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.75
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.75
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.75
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.75
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.75
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.75
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.75
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.75
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.75
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.75
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.75
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.75
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.75
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.75
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.75
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.75
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.75
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.75
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.75
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.75
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.75
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.75
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.75
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.75
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.75
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.75
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.75
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.75
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.75
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.75
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.75
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.75
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.75
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.75
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.75
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.75
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.75
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.75
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.75
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.75
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.76
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 388.73/118.76
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 388.73/118.76
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.76
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.76
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.76
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.76
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.76
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.76
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.76
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.76
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.76
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.76
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.76
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.76
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.76
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.76
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.76
S(mark(z0)) → c32(S(z0)) 388.73/118.76
S(ok(z0)) → c33(S(z0)) 388.73/118.76
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.76
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.76
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.76
PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) 388.73/118.76
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.76
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.76
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.76
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.76
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.76
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.76
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.76
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.76
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.76
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.76
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.76
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.76
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.76
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.76
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.76
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.76
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.76
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.76
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.76
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.76
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.76
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.76
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.76
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.76
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.76
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.76
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.76
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.76
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.76
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.76
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.76
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.76
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.76
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.76
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.76
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.76
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.76
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.76
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.76
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.76
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.76
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.76
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.76
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.76
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.76
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.76
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.76
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.76
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.76
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.76
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.76
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.76
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.76
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.76
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.76
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.76
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.76
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.76
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.76
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.76
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.76
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.76
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.76
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.76
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.76
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.76
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.76
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.76
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.76
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.76
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.76
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.76
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.76
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.76
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.76
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.76
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.76
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.76
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.76
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.76
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.76
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.76
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.76
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.76
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.76
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.76
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.76
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.76
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.76
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.76
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.76
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.76
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.76
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.76
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.76
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.76
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.76
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.76
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.76
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.76
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.76
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.76
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.76
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.76
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.76
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.76
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.76
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.76
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.76
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.76
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.76
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.76
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.76
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.76
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.76
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.76
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.76
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.76
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.76
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.76
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.76
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.76
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.76
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.76
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.76
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.76
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.76
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.76
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.76
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.76
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.76
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.76
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.76
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.76
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.76
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.76
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.76
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.76
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.76
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.76
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.76
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.76
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.76
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.76
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.76
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.76
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.76
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.76
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.76
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.76
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.76
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.76
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.76
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.76
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.76
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.76
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.76
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.76
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.76
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.76
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.76
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.76
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.76
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.76
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.76
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.76
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.76
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.76
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.76
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.76
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.76
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.76
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.76
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.76
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.76
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.76
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.76
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.76
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.76
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.76
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.76
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.76
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.76
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.76
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.76
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.76
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.76
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.76
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.76
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.76
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.76
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.76
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.76
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.76
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.76
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.76
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.76
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.76
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.76
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.76
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.76
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.76
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.76
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.76
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.76
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.76
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.76
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.76
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.76
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.76
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.76
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.76
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.76
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.76
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.76
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.76
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.76
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.76
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.76
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.76
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.76
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.76
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.76
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.76
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.76
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.76
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.76
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.76
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.76
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.76
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.76
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.76
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.76
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.76
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.76
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.76
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.76
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.76
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.76
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.76
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.76
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.76
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.76
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.76
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.76
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.76
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.76
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.76
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.76
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.76
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.76
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.76
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.76
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.76
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.76
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.76
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.76
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.76
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.76
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.76
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.76
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.76
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.76
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.76
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.76
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.76
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 388.73/118.76
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 388.73/118.76
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.76
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.76
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c44, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42, c43, c43

388.73/118.76
388.73/118.76

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

Use narrowing to replace PROPER(U42(z0, z1, z2)) → c44(U42'(proper(z0), proper(z1), proper(z2)), PROPER(z0), PROPER(z1), PROPER(z2)) by

PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.76
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 388.73/118.76
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.76
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.76
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.76
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.76
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.76
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.76
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.76
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.76
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 388.73/118.76
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.76
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 388.73/118.76
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.76
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.76
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.76
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.76
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.76
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.76
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.76
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.76
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 388.73/118.76
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.76
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
388.73/118.76
388.73/118.76

(74) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.73/118.76
active(U12(tt)) → mark(tt) 388.73/118.76
active(U21(tt)) → mark(tt) 388.73/118.76
active(U31(tt, z0)) → mark(z0) 388.73/118.76
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.73/118.76
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.73/118.76
active(isNat(0)) → mark(tt) 388.73/118.76
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.73/118.76
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.73/118.76
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.73/118.76
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.73/118.76
active(U11(z0, z1)) → U11(active(z0), z1) 388.73/118.76
active(U12(z0)) → U12(active(z0)) 388.73/118.76
active(U21(z0)) → U21(active(z0)) 388.73/118.76
active(U31(z0, z1)) → U31(active(z0), z1) 388.73/118.76
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.73/118.76
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.73/118.76
active(s(z0)) → s(active(z0)) 388.73/118.76
active(plus(z0, z1)) → plus(active(z0), z1) 388.73/118.76
active(plus(z0, z1)) → plus(z0, active(z1)) 388.73/118.76
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.73/118.76
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.73/118.76
U12(mark(z0)) → mark(U12(z0)) 388.73/118.76
U12(ok(z0)) → ok(U12(z0)) 388.73/118.76
U21(mark(z0)) → mark(U21(z0)) 388.73/118.76
U21(ok(z0)) → ok(U21(z0)) 388.73/118.78
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.73/118.78
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.73/118.78
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.73/118.78
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.73/118.78
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.73/118.78
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.73/118.78
s(mark(z0)) → mark(s(z0)) 388.73/118.78
s(ok(z0)) → ok(s(z0)) 388.73/118.78
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.73/118.78
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.73/118.78
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.73/118.78
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.73/118.78
proper(tt) → ok(tt) 388.73/118.78
proper(U12(z0)) → U12(proper(z0)) 388.73/118.78
proper(isNat(z0)) → isNat(proper(z0)) 388.73/118.78
proper(U21(z0)) → U21(proper(z0)) 388.73/118.78
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.73/118.78
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.73/118.78
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.73/118.78
proper(s(z0)) → s(proper(z0)) 388.73/118.78
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.73/118.78
proper(0) → ok(0) 388.73/118.78
isNat(ok(z0)) → ok(isNat(z0)) 388.73/118.78
top(mark(z0)) → top(proper(z0)) 388.73/118.78
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.78
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.78
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.78
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.78
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.78
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.78
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.78
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.78
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.78
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.78
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.78
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.78
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.78
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.78
S(mark(z0)) → c32(S(z0)) 388.73/118.78
S(ok(z0)) → c33(S(z0)) 388.73/118.78
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.78
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.78
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.78
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.78
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.78
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.78
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.78
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.78
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.78
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.78
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.78
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.78
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.78
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.78
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.78
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.78
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.78
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.78
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.78
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.78
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.78
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.78
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.78
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.78
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.78
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.78
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.78
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.78
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.78
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.78
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.78
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.78
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.78
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.78
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.78
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.78
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.78
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.78
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.78
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.78
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.78
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.78
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.78
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.78
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.78
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.78
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.78
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.78
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.78
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.78
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.78
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.78
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.78
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.78
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.78
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.78
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.78
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.78
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.78
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.78
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.78
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.78
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.78
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.78
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.78
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.78
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.78
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.78
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.78
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.78
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.78
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.78
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.78
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.78
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.78
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.78
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.78
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.78
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.78
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.78
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.78
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.78
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.78
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.78
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.78
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.78
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.78
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.78
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.78
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.78
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.78
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.78
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.78
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.78
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.78
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.78
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.78
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.78
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.78
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.78
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.78
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.78
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.78
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.78
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.78
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.78
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.78
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.78
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.78
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.78
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.78
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.78
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.78
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.78
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.78
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 388.73/118.78
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 388.73/118.78
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.78
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 388.73/118.78
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.78
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.78
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.78
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.78
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 388.73/118.78
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 388.73/118.78
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.78
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.78
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.78
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.78
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.78
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.78
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.78
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.78
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.78
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.78
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.78
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.78
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.78
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.78
S(mark(z0)) → c32(S(z0)) 388.73/118.78
S(ok(z0)) → c33(S(z0)) 388.73/118.78
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.78
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.78
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.78
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.78
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.78
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.78
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.78
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.78
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.78
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.78
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.78
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.78
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.78
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.78
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.78
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.78
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.78
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.78
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.78
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.78
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.78
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.78
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.78
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.78
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.78
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.78
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.78
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.78
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.78
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.78
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.78
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.78
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.78
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.78
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.78
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.78
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.78
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.78
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.78
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.78
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.78
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.78
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.78
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.78
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.78
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.78
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.78
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.78
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.78
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.78
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.78
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.78
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.78
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.78
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.78
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.78
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.78
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.78
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.78
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.78
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.78
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.78
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.78
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.78
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.78
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.78
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.78
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.78
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.78
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.78
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.78
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.78
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.78
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.78
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.78
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.78
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.78
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.78
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.78
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.78
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.78
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.78
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.78
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.78
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.78
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.78
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.78
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.78
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.78
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.78
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.78
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.78
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.78
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.78
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.78
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.78
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.78
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.78
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.78
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.78
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.78
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.78
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.78
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.78
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.78
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.78
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.78
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.78
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.78
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.78
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.78
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.78
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.78
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.78
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.78
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 388.73/118.78
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 388.73/118.78
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.78
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.78
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1), PROPER(tt)) 388.73/118.78
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.78
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.78
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.78
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.78
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1), PROPER(0)) 388.73/118.78
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(tt), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.78
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(0), PROPER(x2)) 388.73/118.78
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(tt), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.78
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(0), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42, c43, c43, c44

388.73/118.78
388.73/118.78

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

Removed 6 trailing tuple parts
388.73/118.78
388.73/118.78

(76) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.73/118.78
active(U12(tt)) → mark(tt) 388.73/118.78
active(U21(tt)) → mark(tt) 388.73/118.78
active(U31(tt, z0)) → mark(z0) 388.73/118.78
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.73/118.78
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.73/118.78
active(isNat(0)) → mark(tt) 388.73/118.78
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.73/118.78
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.73/118.78
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.73/118.78
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.73/118.78
active(U11(z0, z1)) → U11(active(z0), z1) 388.73/118.78
active(U12(z0)) → U12(active(z0)) 388.73/118.78
active(U21(z0)) → U21(active(z0)) 388.73/118.78
active(U31(z0, z1)) → U31(active(z0), z1) 388.73/118.78
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.73/118.78
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.73/118.78
active(s(z0)) → s(active(z0)) 388.73/118.78
active(plus(z0, z1)) → plus(active(z0), z1) 388.73/118.78
active(plus(z0, z1)) → plus(z0, active(z1)) 388.73/118.78
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.73/118.78
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.73/118.78
U12(mark(z0)) → mark(U12(z0)) 388.73/118.78
U12(ok(z0)) → ok(U12(z0)) 388.73/118.78
U21(mark(z0)) → mark(U21(z0)) 388.73/118.78
U21(ok(z0)) → ok(U21(z0)) 388.73/118.78
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.73/118.78
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.73/118.78
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.73/118.78
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.73/118.78
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.73/118.78
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.73/118.78
s(mark(z0)) → mark(s(z0)) 388.73/118.78
s(ok(z0)) → ok(s(z0)) 388.73/118.78
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.73/118.78
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.73/118.78
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.73/118.78
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.73/118.78
proper(tt) → ok(tt) 388.73/118.78
proper(U12(z0)) → U12(proper(z0)) 388.73/118.78
proper(isNat(z0)) → isNat(proper(z0)) 388.73/118.78
proper(U21(z0)) → U21(proper(z0)) 388.73/118.78
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.73/118.78
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.73/118.78
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.73/118.78
proper(s(z0)) → s(proper(z0)) 388.73/118.78
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.73/118.78
proper(0) → ok(0) 388.73/118.78
isNat(ok(z0)) → ok(isNat(z0)) 388.73/118.78
top(mark(z0)) → top(proper(z0)) 388.73/118.78
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.78
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.78
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.78
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.78
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.78
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.78
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.78
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.78
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.78
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.78
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.78
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.78
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.78
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.78
S(mark(z0)) → c32(S(z0)) 388.73/118.78
S(ok(z0)) → c33(S(z0)) 388.73/118.78
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.78
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.78
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.78
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.78
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.78
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.78
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.78
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.78
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.78
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.78
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.78
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.78
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.78
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.78
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.78
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.78
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.78
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.78
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.78
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.78
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.78
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.78
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.78
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.78
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.78
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.78
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.78
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.78
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.78
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.78
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.78
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.78
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.78
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.78
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.78
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.78
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.78
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.78
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.78
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.78
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.78
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.78
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.78
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.78
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.78
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.78
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.78
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.78
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.78
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.78
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.78
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.78
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.78
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.78
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.78
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.78
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.78
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.78
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.78
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.78
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.78
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.78
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.78
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.78
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.78
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.78
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.78
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.78
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.78
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.78
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.78
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.78
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.78
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.78
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.78
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.78
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.78
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.78
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.78
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.78
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.78
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.78
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.78
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.78
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.78
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.78
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.78
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.78
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.78
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.78
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.78
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.78
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.78
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.78
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.78
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.78
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.78
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.78
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.78
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.78
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.78
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.78
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.78
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.78
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.78
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.78
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.78
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.78
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.78
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.78
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.78
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.78
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.78
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.78
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.78
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.78
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.78
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.78
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.78
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.78
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.78
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.78
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.78
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.78
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.78
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.78
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.78
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.78
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.78
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.78
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.79
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.79
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.79
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.79
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.79
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.79
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.79
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.79
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.79
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.79
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.79
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.79
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.79
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.79
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.79
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.79
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.79
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.79
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.79
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.79
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.79
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.79
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.79
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.79
S(mark(z0)) → c32(S(z0)) 388.73/118.79
S(ok(z0)) → c33(S(z0)) 388.73/118.79
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.79
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.79
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.79
PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) 388.73/118.79
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.79
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.79
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.79
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.79
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.79
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.79
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.79
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.79
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.79
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.79
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.79
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.79
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.79
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.79
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.79
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.79
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.79
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.79
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.79
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.79
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.79
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.79
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.79
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.79
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.79
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.79
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.79
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.79
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.79
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.79
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.79
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.79
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.79
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.79
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.79
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.79
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.79
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.79
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.79
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.79
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.79
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.79
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.79
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.79
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.79
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.79
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.79
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.79
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.79
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.79
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.79
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.79
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.79
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.79
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.79
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.79
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.79
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.79
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.79
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.79
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.79
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.79
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.79
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.79
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.79
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.79
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.79
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.79
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.79
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.79
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.79
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.79
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.79
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.79
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.79
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.79
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.79
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.79
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.79
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.79
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.79
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.79
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.79
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.79
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.79
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.79
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.79
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.79
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.79
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.79
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.79
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.79
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.79
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.79
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.79
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.79
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.79
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.79
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.79
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.79
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.79
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.79
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.79
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c45, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42, c43, c43, c44, c44

388.73/118.79
388.73/118.79

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

Use narrowing to replace PROPER(s(z0)) → c45(S(proper(z0)), PROPER(z0)) by

PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(s(tt)) → c45(S(ok(tt)), PROPER(tt)) 388.73/118.79
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.79
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.79
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.79
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 388.73/118.79
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(s(0)) → c45(S(ok(0)), PROPER(0))
388.73/118.79
388.73/118.79

(78) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 388.73/118.79
active(U12(tt)) → mark(tt) 388.73/118.79
active(U21(tt)) → mark(tt) 388.73/118.79
active(U31(tt, z0)) → mark(z0) 388.73/118.79
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 388.73/118.79
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 388.73/118.79
active(isNat(0)) → mark(tt) 388.73/118.79
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 388.73/118.79
active(isNat(s(z0))) → mark(U21(isNat(z0))) 388.73/118.79
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 388.73/118.79
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 388.73/118.79
active(U11(z0, z1)) → U11(active(z0), z1) 388.73/118.79
active(U12(z0)) → U12(active(z0)) 388.73/118.79
active(U21(z0)) → U21(active(z0)) 388.73/118.79
active(U31(z0, z1)) → U31(active(z0), z1) 388.73/118.79
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 388.73/118.79
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 388.73/118.79
active(s(z0)) → s(active(z0)) 388.73/118.79
active(plus(z0, z1)) → plus(active(z0), z1) 388.73/118.79
active(plus(z0, z1)) → plus(z0, active(z1)) 388.73/118.79
U11(mark(z0), z1) → mark(U11(z0, z1)) 388.73/118.79
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 388.73/118.79
U12(mark(z0)) → mark(U12(z0)) 388.73/118.79
U12(ok(z0)) → ok(U12(z0)) 388.73/118.79
U21(mark(z0)) → mark(U21(z0)) 388.73/118.79
U21(ok(z0)) → ok(U21(z0)) 388.73/118.79
U31(mark(z0), z1) → mark(U31(z0, z1)) 388.73/118.79
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 388.73/118.79
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 388.73/118.79
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 388.73/118.79
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 388.73/118.79
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 388.73/118.79
s(mark(z0)) → mark(s(z0)) 388.73/118.79
s(ok(z0)) → ok(s(z0)) 388.73/118.79
plus(mark(z0), z1) → mark(plus(z0, z1)) 388.73/118.79
plus(z0, mark(z1)) → mark(plus(z0, z1)) 388.73/118.79
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 388.73/118.79
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 388.73/118.79
proper(tt) → ok(tt) 388.73/118.79
proper(U12(z0)) → U12(proper(z0)) 388.73/118.79
proper(isNat(z0)) → isNat(proper(z0)) 388.73/118.79
proper(U21(z0)) → U21(proper(z0)) 388.73/118.79
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 388.73/118.79
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 388.73/118.79
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 388.73/118.79
proper(s(z0)) → s(proper(z0)) 388.73/118.79
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 388.73/118.79
proper(0) → ok(0) 388.73/118.79
isNat(ok(z0)) → ok(isNat(z0)) 388.73/118.79
top(mark(z0)) → top(proper(z0)) 388.73/118.79
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.79
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.79
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.79
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.79
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.79
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.79
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.79
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.79
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.79
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.79
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.79
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.79
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.79
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.79
S(mark(z0)) → c32(S(z0)) 388.73/118.79
S(ok(z0)) → c33(S(z0)) 388.73/118.79
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.79
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.79
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.79
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.79
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.79
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.79
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.79
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.79
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.79
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.79
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.79
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.79
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.79
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.79
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.79
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.79
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.79
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.79
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.79
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.79
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.79
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.79
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.79
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.79
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.79
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.79
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.79
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.79
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.79
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.79
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.79
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.79
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.79
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.79
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.79
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.79
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.79
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.79
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.79
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.79
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.79
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.79
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.79
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.79
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.79
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.79
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.79
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.79
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.79
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.79
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.79
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.79
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.79
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.79
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.79
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.79
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.79
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.79
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.79
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.79
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.79
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.79
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.79
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.79
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.79
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.79
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.79
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.79
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.79
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.79
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.79
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.79
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.79
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.79
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.79
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.79
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.79
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.79
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.79
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.79
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.79
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.79
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.79
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.79
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.79
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.79
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.79
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.79
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.79
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.79
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.79
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.79
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.79
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.79
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.79
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.79
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.79
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.79
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.79
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.79
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.79
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.79
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.79
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.79
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.79
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.79
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.79
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 388.73/118.79
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.79
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.79
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(s(tt)) → c45(S(ok(tt)), PROPER(tt)) 388.73/118.79
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.79
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.79
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.79
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 388.73/118.79
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(s(0)) → c45(S(ok(0)), PROPER(0))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 388.73/118.79
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 388.73/118.79
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 388.73/118.79
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 388.73/118.79
U12'(mark(z0)) → c22(U12'(z0)) 388.73/118.79
U12'(ok(z0)) → c23(U12'(z0)) 388.73/118.79
U21'(mark(z0)) → c24(U21'(z0)) 388.73/118.79
U21'(ok(z0)) → c25(U21'(z0)) 388.73/118.79
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 388.73/118.79
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 388.73/118.79
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 388.73/118.79
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 388.73/118.79
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 388.73/118.79
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 388.73/118.79
S(mark(z0)) → c32(S(z0)) 388.73/118.79
S(ok(z0)) → c33(S(z0)) 388.73/118.79
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 388.73/118.79
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 388.73/118.79
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 388.73/118.79
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 388.73/118.79
ISNAT(ok(z0)) → c48(ISNAT(z0)) 388.73/118.79
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 388.73/118.79
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 388.73/118.79
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 388.73/118.79
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 388.73/118.79
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 388.73/118.79
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 388.73/118.79
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 388.73/118.79
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 388.73/118.79
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 388.73/118.79
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 388.73/118.79
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 388.73/118.79
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 388.73/118.79
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 388.73/118.79
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 388.73/118.79
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.79
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.79
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.79
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 388.73/118.79
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 388.73/118.79
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 388.73/118.79
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 388.73/118.79
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 388.73/118.79
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 388.73/118.79
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 388.73/118.79
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 388.73/118.79
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 388.73/118.79
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 388.73/118.79
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 388.73/118.79
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 388.73/118.79
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 388.73/118.79
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 388.73/118.79
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 388.73/118.79
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 388.73/118.79
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.79
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.79
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 388.73/118.79
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 388.73/118.79
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 388.73/118.79
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 388.73/118.79
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 388.73/118.79
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.79
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.79
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 388.73/118.79
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 388.73/118.79
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.79
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.79
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 388.73/118.79
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 388.73/118.79
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 388.73/118.79
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 388.73/118.79
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 388.73/118.79
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 388.73/118.79
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.79
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 388.73/118.79
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 388.73/118.79
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 388.73/118.79
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 388.73/118.79
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 388.73/118.79
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 388.73/118.79
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 388.73/118.79
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 388.73/118.79
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 388.73/118.79
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 388.73/118.79
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 388.73/118.79
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 388.73/118.79
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 388.73/118.79
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 388.73/118.79
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 388.73/118.79
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 388.73/118.79
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 388.73/118.79
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 388.73/118.79
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 388.73/118.79
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 388.73/118.79
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 388.73/118.79
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 388.73/118.79
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 388.73/118.79
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 388.73/118.79
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 388.73/118.79
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 388.73/118.79
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 388.73/118.79
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 388.73/118.79
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 388.73/118.79
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.79
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.79
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.79
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.79
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.79
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.79
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.79
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.79
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.79
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.79
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 388.73/118.79
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U12(tt)) → c39(U12'(ok(tt))) 388.73/118.79
PROPER(U12(0)) → c39(U12'(ok(0))) 388.73/118.79
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.79
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.79
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.79
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 388.73/118.79
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 388.73/118.79
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 388.73/118.79
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 388.73/118.79
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 388.73/118.79
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 388.73/118.79
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 388.73/118.79
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U21(tt)) → c41(U21'(ok(tt))) 388.73/118.79
PROPER(U21(0)) → c41(U21'(ok(0))) 388.73/118.79
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 388.73/118.79
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 388.73/118.79
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 388.73/118.79
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 388.73/118.79
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 388.73/118.79
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 388.73/118.79
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 388.73/118.79
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 388.73/118.79
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 388.73/118.79
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 388.73/118.79
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 388.73/118.79
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 388.73/118.79
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 388.73/118.79
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 388.73/118.79
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 388.73/118.79
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.80
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.80
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.80
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.80
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.80
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.80
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.80
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.80
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.80
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.80
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.80
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.80
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.80
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.80
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.80
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.80
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.80
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.80
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 388.73/118.80
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 388.73/118.80
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.80
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 388.73/118.80
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 388.73/118.80
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 388.73/118.80
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 388.73/118.80
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 388.73/118.80
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 388.73/118.80
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 388.73/118.80
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 388.73/118.80
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 388.73/118.80
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 388.73/118.80
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 388.73/118.80
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 388.73/118.80
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 388.73/118.80
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 388.73/118.80
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 388.73/118.80
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 388.73/118.80
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 388.73/118.80
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 388.73/118.80
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 388.73/118.80
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 388.73/118.80
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.82
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.82
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.82
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(s(tt)) → c45(S(ok(tt)), PROPER(tt)) 389.10/118.82
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.82
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.82
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.82
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.82
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(s(0)) → c45(S(ok(0)), PROPER(0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42, c43, c43, c44, c44, c45

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

Removed 2 trailing tuple parts
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(80) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.82
active(U12(tt)) → mark(tt) 389.10/118.82
active(U21(tt)) → mark(tt) 389.10/118.82
active(U31(tt, z0)) → mark(z0) 389.10/118.82
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.82
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.82
active(isNat(0)) → mark(tt) 389.10/118.82
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.82
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.82
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.82
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.82
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.82
active(U12(z0)) → U12(active(z0)) 389.10/118.82
active(U21(z0)) → U21(active(z0)) 389.10/118.82
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.82
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.82
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.82
active(s(z0)) → s(active(z0)) 389.10/118.82
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.82
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.82
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.82
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.82
U12(mark(z0)) → mark(U12(z0)) 389.10/118.82
U12(ok(z0)) → ok(U12(z0)) 389.10/118.82
U21(mark(z0)) → mark(U21(z0)) 389.10/118.82
U21(ok(z0)) → ok(U21(z0)) 389.10/118.82
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.82
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.82
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.82
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.82
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.82
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.82
s(mark(z0)) → mark(s(z0)) 389.10/118.82
s(ok(z0)) → ok(s(z0)) 389.10/118.82
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.82
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.82
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.82
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.82
proper(tt) → ok(tt) 389.10/118.82
proper(U12(z0)) → U12(proper(z0)) 389.10/118.82
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.82
proper(U21(z0)) → U21(proper(z0)) 389.10/118.82
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.82
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.82
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.82
proper(s(z0)) → s(proper(z0)) 389.10/118.82
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.82
proper(0) → ok(0) 389.10/118.82
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.82
top(mark(z0)) → top(proper(z0)) 389.10/118.82
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.82
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.82
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.82
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.82
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.82
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.82
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.82
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.82
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.82
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.82
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.82
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.82
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.82
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.82
S(mark(z0)) → c32(S(z0)) 389.10/118.82
S(ok(z0)) → c33(S(z0)) 389.10/118.82
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.82
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.82
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.82
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 389.10/118.82
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.82
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 389.10/118.82
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 389.10/118.82
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.82
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.82
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.82
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.82
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.82
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.82
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.82
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.82
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.82
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.82
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.82
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.82
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.82
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.82
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.82
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.82
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.82
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.82
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.82
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.82
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.82
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.82
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.82
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.82
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.82
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.82
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.82
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.82
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.82
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.82
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.82
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.82
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.82
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.82
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.82
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.82
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.82
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.82
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.82
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.82
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.82
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.82
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.82
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.82
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.82
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.82
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.82
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.82
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.82
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.82
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.82
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.82
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.82
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.82
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.82
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.82
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.82
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.82
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.82
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.82
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.82
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.82
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.82
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.82
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.82
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.82
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.82
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.82
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.82
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.82
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.82
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.82
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.82
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.82
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.82
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.82
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.82
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.82
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.82
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.82
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.82
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.82
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.82
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.82
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.82
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.82
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.82
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.82
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.82
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.82
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.82
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.82
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.82
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.82
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.82
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.82
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.82
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.82
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.82
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.82
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.82
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.82
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.82
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.82
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.82
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.82
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.82
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.82
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.82
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.82
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.82
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.82
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.82
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.82
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.82
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.82
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.82
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.82
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.82
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.82
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.82
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.82
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.82
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.82
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.82
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.82
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.82
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.82
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.82
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.82
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.82
PROPER(s(0)) → c45(S(ok(0)))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.82
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.82
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.82
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.82
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.82
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.82
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.82
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.82
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.82
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.82
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.82
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.82
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.82
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.82
S(mark(z0)) → c32(S(z0)) 389.10/118.82
S(ok(z0)) → c33(S(z0)) 389.10/118.82
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.82
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.82
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.82
PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) 389.10/118.82
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.82
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 389.10/118.82
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 389.10/118.82
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.82
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.82
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.82
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.82
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.82
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.82
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.82
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.82
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.82
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.82
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.82
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.82
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.82
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.82
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.82
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.82
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.82
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.82
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.82
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.82
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.82
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.82
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.82
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.82
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.82
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.82
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.82
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.82
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.82
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.82
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.82
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.82
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.82
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.82
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.82
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.82
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.82
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.82
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.82
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.82
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.82
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.82
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.82
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.82
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.82
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.82
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.82
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.82
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.82
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.82
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.82
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.82
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.82
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.82
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.82
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.82
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.82
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.82
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.82
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.82
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.82
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.82
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.82
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.82
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.82
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.82
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.82
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.82
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.82
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.82
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.82
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.82
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.82
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.82
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.82
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.82
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.82
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.82
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.82
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.82
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.82
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.82
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.82
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.82
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.82
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.82
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.82
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.82
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.82
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.82
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.82
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.82
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.82
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.82
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.82
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.82
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.82
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.82
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.82
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.82
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.82
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.82
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.82
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.82
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.82
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.82
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.82
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.82
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.82
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.82
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.82
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.82
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.82
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.82
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.82
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.82
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.82
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.82
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.82
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.82
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.82
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.82
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.82
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.82
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.82
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.82
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.82
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.82
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.82
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.82
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.82
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.82
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.82
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.82
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.82
PROPER(s(0)) → c45(S(ok(0)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, PROPER, ISNAT, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c46, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42, c43, c43, c44, c44, c45, c45

389.10/118.82
389.10/118.82

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

Use narrowing to replace PROPER(plus(z0, z1)) → c46(PLUS(proper(z0), proper(z1)), PROPER(z0), PROPER(z1)) by

PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.82
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 389.10/118.82
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.82
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.82
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.82
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.82
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.82
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.82
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.82
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.82
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 389.10/118.82
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 389.10/118.82
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.82
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.82
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.82
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.82
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.82
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.82
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.82
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
389.10/118.82
389.10/118.82

(82) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.82
active(U12(tt)) → mark(tt) 389.10/118.82
active(U21(tt)) → mark(tt) 389.10/118.82
active(U31(tt, z0)) → mark(z0) 389.10/118.82
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.82
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.82
active(isNat(0)) → mark(tt) 389.10/118.82
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.82
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.82
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.82
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.82
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.82
active(U12(z0)) → U12(active(z0)) 389.10/118.82
active(U21(z0)) → U21(active(z0)) 389.10/118.82
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.82
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.82
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.82
active(s(z0)) → s(active(z0)) 389.10/118.82
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.82
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.82
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.82
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.82
U12(mark(z0)) → mark(U12(z0)) 389.10/118.82
U12(ok(z0)) → ok(U12(z0)) 389.10/118.82
U21(mark(z0)) → mark(U21(z0)) 389.10/118.82
U21(ok(z0)) → ok(U21(z0)) 389.10/118.82
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.82
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.82
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.82
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.82
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.82
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.82
s(mark(z0)) → mark(s(z0)) 389.10/118.82
s(ok(z0)) → ok(s(z0)) 389.10/118.82
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.82
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.82
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.82
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.82
proper(tt) → ok(tt) 389.10/118.82
proper(U12(z0)) → U12(proper(z0)) 389.10/118.82
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.82
proper(U21(z0)) → U21(proper(z0)) 389.10/118.82
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.82
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.82
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.82
proper(s(z0)) → s(proper(z0)) 389.10/118.82
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.82
proper(0) → ok(0) 389.10/118.82
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.82
top(mark(z0)) → top(proper(z0)) 389.10/118.82
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.82
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.82
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.82
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.82
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.82
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.82
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.82
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.82
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.82
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.82
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.82
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.82
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.82
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.82
S(mark(z0)) → c32(S(z0)) 389.10/118.82
S(ok(z0)) → c33(S(z0)) 389.10/118.82
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.82
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.82
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.82
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.82
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 389.10/118.82
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 389.10/118.82
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.82
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.82
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.82
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.82
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.82
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.82
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.82
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.82
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.82
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.82
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.82
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.82
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.82
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.82
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.82
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.82
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.82
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.82
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.82
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.82
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.82
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.82
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.82
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.82
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.82
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.82
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.82
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.82
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.82
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.82
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.82
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.82
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.82
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.82
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.82
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.82
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.82
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.82
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.82
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.82
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.82
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.82
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.82
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.82
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.82
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.82
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.82
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.82
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.82
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.82
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.82
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.82
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.82
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.82
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.82
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.82
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.82
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.82
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.82
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.82
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.82
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.82
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.82
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.82
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.82
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.82
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.82
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.82
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.82
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.83
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.83
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.83
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.83
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.83
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.83
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.83
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.83
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.83
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.83
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.83
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.83
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.83
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.83
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.83
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.83
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.83
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.83
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.83
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.83
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.83
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.83
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.83
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.83
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.83
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.83
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.83
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.83
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.83
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.83
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.83
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.83
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.83
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.83
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.83
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.83
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.83
PROPER(s(0)) → c45(S(ok(0))) 389.10/118.83
PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 389.10/118.83
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.83
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.83
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.83
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.83
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 389.10/118.83
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 389.10/118.83
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.83
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.83
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.83
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.83
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.83
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.83
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.83
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.83
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.83
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.83
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.83
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.83
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.83
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.83
S(mark(z0)) → c32(S(z0)) 389.10/118.83
S(ok(z0)) → c33(S(z0)) 389.10/118.83
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.83
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.83
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.83
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.83
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 389.10/118.83
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 389.10/118.83
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.83
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.83
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.83
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.83
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.83
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.83
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.83
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.83
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.83
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.83
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.83
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.83
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.83
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.83
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.83
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.83
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.83
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.83
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.83
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.83
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.83
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.83
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.83
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.83
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.83
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.83
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.83
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.83
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.83
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.83
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.83
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.83
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.83
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.83
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.83
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.83
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.83
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.83
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.83
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.83
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.83
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.83
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.83
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.83
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.83
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.83
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.83
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.83
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.83
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.83
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.83
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.83
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.83
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.83
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.83
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.83
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.83
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.83
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.83
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.83
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.83
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.83
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.83
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.83
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.83
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.83
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.83
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.83
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.83
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.83
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.83
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.83
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.83
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.83
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.83
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.83
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.83
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.83
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.83
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.83
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.83
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.83
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.83
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.83
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.83
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.83
PROPER(s(0)) → c45(S(ok(0))) 389.10/118.83
PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0), PROPER(tt)) 389.10/118.83
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.83
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.83
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.83
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.83
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0), PROPER(0)) 389.10/118.83
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(tt), PROPER(x1)) 389.10/118.83
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(0), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT, TOP, PROPER

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42, c43, c43, c44, c44, c45, c45, c46

389.10/118.83
389.10/118.83

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

Removed 4 trailing tuple parts
389.10/118.83
389.10/118.83

(84) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.83
active(U12(tt)) → mark(tt) 389.10/118.83
active(U21(tt)) → mark(tt) 389.10/118.83
active(U31(tt, z0)) → mark(z0) 389.10/118.83
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.83
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.83
active(isNat(0)) → mark(tt) 389.10/118.83
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.83
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.83
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.83
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.83
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.83
active(U12(z0)) → U12(active(z0)) 389.10/118.83
active(U21(z0)) → U21(active(z0)) 389.10/118.83
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.83
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.83
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.83
active(s(z0)) → s(active(z0)) 389.10/118.83
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.83
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.83
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.83
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.83
U12(mark(z0)) → mark(U12(z0)) 389.10/118.83
U12(ok(z0)) → ok(U12(z0)) 389.10/118.83
U21(mark(z0)) → mark(U21(z0)) 389.10/118.83
U21(ok(z0)) → ok(U21(z0)) 389.10/118.83
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.83
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.83
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.83
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.83
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.83
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.83
s(mark(z0)) → mark(s(z0)) 389.10/118.83
s(ok(z0)) → ok(s(z0)) 389.10/118.83
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.83
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.83
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.83
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.83
proper(tt) → ok(tt) 389.10/118.83
proper(U12(z0)) → U12(proper(z0)) 389.10/118.83
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.83
proper(U21(z0)) → U21(proper(z0)) 389.10/118.83
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.83
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.83
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.83
proper(s(z0)) → s(proper(z0)) 389.10/118.83
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.83
proper(0) → ok(0) 389.10/118.83
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.83
top(mark(z0)) → top(proper(z0)) 389.10/118.83
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.83
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.83
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.83
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.83
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.83
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.83
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.83
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.83
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.83
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.83
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.83
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.83
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.83
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.83
S(mark(z0)) → c32(S(z0)) 389.10/118.83
S(ok(z0)) → c33(S(z0)) 389.10/118.83
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.83
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.83
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.83
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.83
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 389.10/118.83
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 389.10/118.83
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.83
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.83
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.83
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.83
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.83
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.83
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.83
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.83
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.83
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.83
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.83
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.83
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.83
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.83
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.83
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.83
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.83
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.83
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.83
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.83
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.83
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.83
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.83
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.83
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.83
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.83
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.83
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.83
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.83
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.83
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.83
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.83
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.83
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.83
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.83
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.83
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.83
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.83
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.83
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.83
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.83
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.83
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.83
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.83
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.83
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.83
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.83
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.83
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.83
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.83
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.83
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.83
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.83
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.83
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.83
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.83
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.83
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.83
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.83
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.83
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.83
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.83
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.83
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.83
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.83
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.83
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.83
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.83
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.83
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.83
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.83
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.83
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.83
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.83
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.83
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.83
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.83
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.83
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.83
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.83
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.83
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.83
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.83
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.83
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.83
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.83
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.83
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.83
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.83
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.83
PROPER(s(0)) → c45(S(ok(0))) 389.10/118.83
PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.83
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.83
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.83
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.83
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.83
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.83
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0)) 389.10/118.83
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(x1))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.83
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.83
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.83
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.83
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.83
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.83
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.83
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.83
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.83
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.83
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.83
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.83
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.83
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.83
S(mark(z0)) → c32(S(z0)) 389.10/118.83
S(ok(z0)) → c33(S(z0)) 389.10/118.83
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.83
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.83
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.83
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.83
TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) 389.10/118.83
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 389.10/118.83
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.83
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.83
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.83
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.83
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.83
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.83
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.83
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.83
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.83
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.83
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.83
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.83
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.83
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.83
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.83
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.83
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.83
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.83
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.83
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.83
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.83
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.83
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.83
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.83
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.83
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.83
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.83
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.83
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.83
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.83
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.83
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.83
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.83
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.83
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.83
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.83
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.83
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.83
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.83
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.83
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.83
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.83
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.83
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.83
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.83
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.83
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.83
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.83
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.83
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.83
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.83
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.83
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.83
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.83
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.83
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.83
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.83
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.83
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.83
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.83
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.83
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.83
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.83
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.83
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.83
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.83
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.83
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.83
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.83
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.83
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.83
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.83
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.83
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.83
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.83
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.83
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.83
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.83
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.83
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.83
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.83
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.83
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.83
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.83
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.83
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.83
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.83
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.83
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.83
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.83
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.83
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.83
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.83
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.83
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.83
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.83
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.83
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.83
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.83
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.83
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.83
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.83
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.83
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.83
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.83
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.83
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.83
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.83
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.83
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.83
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.83
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.83
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.83
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.84
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.84
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.84
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.84
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.84
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.84
PROPER(s(0)) → c45(S(ok(0))) 389.10/118.84
PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.84
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.84
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.84
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.84
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.84
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0)) 389.10/118.84
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(x1))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT, TOP, PROPER

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48, c49, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42, c43, c43, c44, c44, c45, c45, c46, c46

389.10/118.84
389.10/118.84

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

Use narrowing to replace TOP(mark(z0)) → c49(TOP(proper(z0)), PROPER(z0)) by

TOP(mark(U11(z0, z1))) → c49(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
TOP(mark(tt)) → c49(TOP(ok(tt)), PROPER(tt)) 389.10/118.84
TOP(mark(U12(z0))) → c49(TOP(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
TOP(mark(isNat(z0))) → c49(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
TOP(mark(U21(z0))) → c49(TOP(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
TOP(mark(U31(z0, z1))) → c49(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
TOP(mark(U41(z0, z1, z2))) → c49(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
TOP(mark(U42(z0, z1, z2))) → c49(TOP(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
TOP(mark(s(z0))) → c49(TOP(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
TOP(mark(plus(z0, z1))) → c49(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
TOP(mark(0)) → c49(TOP(ok(0)), PROPER(0))
389.10/118.84
389.10/118.84

(86) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.84
active(U12(tt)) → mark(tt) 389.10/118.84
active(U21(tt)) → mark(tt) 389.10/118.84
active(U31(tt, z0)) → mark(z0) 389.10/118.84
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.84
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.84
active(isNat(0)) → mark(tt) 389.10/118.84
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.84
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.84
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.84
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.84
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.84
active(U12(z0)) → U12(active(z0)) 389.10/118.84
active(U21(z0)) → U21(active(z0)) 389.10/118.84
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.84
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.84
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.84
active(s(z0)) → s(active(z0)) 389.10/118.84
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.84
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.84
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.84
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.84
U12(mark(z0)) → mark(U12(z0)) 389.10/118.84
U12(ok(z0)) → ok(U12(z0)) 389.10/118.84
U21(mark(z0)) → mark(U21(z0)) 389.10/118.84
U21(ok(z0)) → ok(U21(z0)) 389.10/118.84
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.84
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.84
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.84
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.84
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.84
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.84
s(mark(z0)) → mark(s(z0)) 389.10/118.84
s(ok(z0)) → ok(s(z0)) 389.10/118.84
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.84
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.84
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.84
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.84
proper(tt) → ok(tt) 389.10/118.84
proper(U12(z0)) → U12(proper(z0)) 389.10/118.84
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.84
proper(U21(z0)) → U21(proper(z0)) 389.10/118.84
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.84
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.84
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.84
proper(s(z0)) → s(proper(z0)) 389.10/118.84
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.84
proper(0) → ok(0) 389.10/118.84
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.84
top(mark(z0)) → top(proper(z0)) 389.10/118.84
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.84
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.84
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.84
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.84
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.84
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.84
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.84
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.84
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.84
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.84
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.84
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.84
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.84
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.84
S(mark(z0)) → c32(S(z0)) 389.10/118.84
S(ok(z0)) → c33(S(z0)) 389.10/118.84
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.84
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.84
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.84
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.84
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 389.10/118.84
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.84
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.84
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.84
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.84
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.84
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.84
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.84
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.84
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.84
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.84
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.84
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.84
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.84
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.84
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.84
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.84
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.84
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.84
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.84
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.84
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.84
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.84
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.84
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.84
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.84
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.84
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.84
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.84
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.84
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.84
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.84
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.84
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.84
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.84
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.84
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.84
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.84
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.84
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.84
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.84
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.84
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.84
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.84
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.84
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.84
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.84
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.84
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.84
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.84
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.84
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.84
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.84
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.84
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.84
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.84
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.84
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.84
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.84
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.84
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.84
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.84
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.84
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.84
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.84
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.84
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.84
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.84
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.84
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.84
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.84
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.84
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.84
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.84
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.84
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.84
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.84
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.84
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.84
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.84
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.84
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.84
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.84
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.84
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.84
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.84
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.84
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.84
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.84
PROPER(s(0)) → c45(S(ok(0))) 389.10/118.84
PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.84
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.84
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.84
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.84
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.84
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0)) 389.10/118.84
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(x1)) 389.10/118.84
TOP(mark(U11(z0, z1))) → c49(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
TOP(mark(tt)) → c49(TOP(ok(tt)), PROPER(tt)) 389.10/118.84
TOP(mark(U12(z0))) → c49(TOP(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
TOP(mark(isNat(z0))) → c49(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
TOP(mark(U21(z0))) → c49(TOP(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
TOP(mark(U31(z0, z1))) → c49(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
TOP(mark(U41(z0, z1, z2))) → c49(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
TOP(mark(U42(z0, z1, z2))) → c49(TOP(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
TOP(mark(s(z0))) → c49(TOP(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
TOP(mark(plus(z0, z1))) → c49(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
TOP(mark(0)) → c49(TOP(ok(0)), PROPER(0))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.84
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.84
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.84
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.84
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.84
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.84
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.84
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.84
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.84
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.84
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.84
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.84
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.84
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.84
S(mark(z0)) → c32(S(z0)) 389.10/118.84
S(ok(z0)) → c33(S(z0)) 389.10/118.84
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.84
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.84
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.84
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.84
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 389.10/118.84
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.84
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.84
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.84
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.84
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.84
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.84
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.84
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.84
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.84
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.84
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.84
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.84
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.84
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.84
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.84
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.84
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.84
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.84
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.84
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.84
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.84
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.84
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.84
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.84
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.84
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.84
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.84
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.84
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.84
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.84
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.84
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.84
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.84
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.84
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.84
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.84
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.84
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.84
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.84
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.84
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.84
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.84
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.84
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.84
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.84
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.84
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.84
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.84
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.84
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.84
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.84
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.84
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.84
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.84
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.84
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.84
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.84
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.84
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.84
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.84
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.84
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.84
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.84
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.84
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.84
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.84
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.84
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.84
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.84
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.84
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.84
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.84
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.84
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.84
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.84
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.84
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.84
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.84
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.84
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.84
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.84
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.84
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.84
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.84
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.84
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.84
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.84
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.84
PROPER(s(0)) → c45(S(ok(0))) 389.10/118.84
PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.84
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.84
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.84
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.84
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.84
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.84
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0)) 389.10/118.84
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(x1)) 389.10/118.84
TOP(mark(U11(z0, z1))) → c49(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
TOP(mark(tt)) → c49(TOP(ok(tt)), PROPER(tt)) 389.10/118.84
TOP(mark(U12(z0))) → c49(TOP(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
TOP(mark(isNat(z0))) → c49(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
TOP(mark(U21(z0))) → c49(TOP(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
TOP(mark(U31(z0, z1))) → c49(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
TOP(mark(U41(z0, z1, z2))) → c49(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
TOP(mark(U42(z0, z1, z2))) → c49(TOP(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
TOP(mark(s(z0))) → c49(TOP(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
TOP(mark(plus(z0, z1))) → c49(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
TOP(mark(0)) → c49(TOP(ok(0)), PROPER(0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT, TOP, PROPER

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42, c43, c43, c44, c44, c45, c45, c46, c46, c49

389.10/118.84
389.10/118.84

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

Removed 2 trailing tuple parts
389.10/118.84
389.10/118.84

(88) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.84
active(U12(tt)) → mark(tt) 389.10/118.84
active(U21(tt)) → mark(tt) 389.10/118.84
active(U31(tt, z0)) → mark(z0) 389.10/118.84
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.84
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.84
active(isNat(0)) → mark(tt) 389.10/118.84
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.84
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.84
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.84
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.84
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.84
active(U12(z0)) → U12(active(z0)) 389.10/118.84
active(U21(z0)) → U21(active(z0)) 389.10/118.84
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.84
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.84
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.84
active(s(z0)) → s(active(z0)) 389.10/118.84
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.84
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.84
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.84
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.84
U12(mark(z0)) → mark(U12(z0)) 389.10/118.84
U12(ok(z0)) → ok(U12(z0)) 389.10/118.84
U21(mark(z0)) → mark(U21(z0)) 389.10/118.84
U21(ok(z0)) → ok(U21(z0)) 389.10/118.84
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.84
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.84
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.84
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.84
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.84
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.84
s(mark(z0)) → mark(s(z0)) 389.10/118.84
s(ok(z0)) → ok(s(z0)) 389.10/118.84
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.84
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.84
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.84
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.84
proper(tt) → ok(tt) 389.10/118.84
proper(U12(z0)) → U12(proper(z0)) 389.10/118.84
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.84
proper(U21(z0)) → U21(proper(z0)) 389.10/118.84
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.84
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.84
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.84
proper(s(z0)) → s(proper(z0)) 389.10/118.84
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.84
proper(0) → ok(0) 389.10/118.84
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.84
top(mark(z0)) → top(proper(z0)) 389.10/118.84
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.84
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.84
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.84
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.84
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.84
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.84
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.84
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.84
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.84
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.84
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.84
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.84
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.84
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.84
S(mark(z0)) → c32(S(z0)) 389.10/118.84
S(ok(z0)) → c33(S(z0)) 389.10/118.84
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.84
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.84
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.84
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.84
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 389.10/118.84
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.84
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.84
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.84
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.84
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.84
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.84
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.84
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.84
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.84
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.84
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.84
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.84
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.84
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.84
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.84
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.84
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.84
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.84
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.84
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.84
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.84
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.84
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.84
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.84
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.84
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.84
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.84
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.84
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.84
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.84
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.84
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.84
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.84
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.84
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.84
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.84
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.84
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.84
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.84
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.84
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.84
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.84
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.84
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.84
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.84
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.84
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.84
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.84
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.84
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.84
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.84
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.84
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.84
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.84
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.84
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.84
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.84
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.84
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.84
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.84
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.84
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.84
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.84
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.84
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.84
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.84
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.84
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.84
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.84
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.84
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.84
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.84
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.84
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.84
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.84
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.84
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.84
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.84
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.84
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.84
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.84
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.84
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.84
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.84
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.84
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.84
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.84
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.84
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.84
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.84
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.84
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.84
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.84
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.84
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.84
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.84
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.84
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.84
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.84
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.84
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.84
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.84
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.84
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.84
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.84
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.84
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.84
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.84
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.84
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.84
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.84
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.84
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.84
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.84
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.84
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.84
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.84
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.84
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.84
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.84
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.84
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.84
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.84
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.84
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.84
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.85
PROPER(s(0)) → c45(S(ok(0))) 389.10/118.85
PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.85
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.85
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.85
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.85
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.85
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0)) 389.10/118.85
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(x1)) 389.10/118.85
TOP(mark(U11(z0, z1))) → c49(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
TOP(mark(U12(z0))) → c49(TOP(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
TOP(mark(isNat(z0))) → c49(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
TOP(mark(U21(z0))) → c49(TOP(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
TOP(mark(U31(z0, z1))) → c49(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
TOP(mark(U41(z0, z1, z2))) → c49(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
TOP(mark(U42(z0, z1, z2))) → c49(TOP(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
TOP(mark(s(z0))) → c49(TOP(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
TOP(mark(plus(z0, z1))) → c49(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
TOP(mark(tt)) → c49(TOP(ok(tt))) 389.10/118.85
TOP(mark(0)) → c49(TOP(ok(0)))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.85
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.85
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.85
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.85
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.85
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.85
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.85
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.85
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.85
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.85
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.85
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.85
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.85
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.85
S(mark(z0)) → c32(S(z0)) 389.10/118.85
S(ok(z0)) → c33(S(z0)) 389.10/118.85
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.85
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.85
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.85
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.85
TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) 389.10/118.85
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.85
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.85
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.85
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.85
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.85
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.85
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.85
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.85
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.85
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.85
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.85
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.85
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.85
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.85
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.85
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.85
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.85
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.85
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.85
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.85
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.85
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.85
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.85
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.85
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.85
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.85
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.85
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.85
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.85
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.85
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.85
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.85
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.85
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.85
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.85
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.85
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.85
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.85
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.85
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.85
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.85
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.85
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.85
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.85
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.85
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.85
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.85
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.85
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.85
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.85
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.85
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.85
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.85
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.85
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.85
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.85
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.85
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.85
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.85
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.85
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.85
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.85
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.85
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.85
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.85
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.85
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.85
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.85
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.85
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.85
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.85
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.85
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.85
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.85
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.85
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.85
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.85
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.85
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.85
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.85
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.85
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.85
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.85
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.85
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.85
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.85
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.85
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.85
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.85
PROPER(s(0)) → c45(S(ok(0))) 389.10/118.85
PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.85
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.85
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.85
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.85
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.85
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0)) 389.10/118.85
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(x1)) 389.10/118.85
TOP(mark(U11(z0, z1))) → c49(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
TOP(mark(U12(z0))) → c49(TOP(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
TOP(mark(isNat(z0))) → c49(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
TOP(mark(U21(z0))) → c49(TOP(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
TOP(mark(U31(z0, z1))) → c49(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
TOP(mark(U41(z0, z1, z2))) → c49(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
TOP(mark(U42(z0, z1, z2))) → c49(TOP(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
TOP(mark(s(z0))) → c49(TOP(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
TOP(mark(plus(z0, z1))) → c49(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
TOP(mark(tt)) → c49(TOP(ok(tt))) 389.10/118.85
TOP(mark(0)) → c49(TOP(ok(0)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT, TOP, PROPER

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48, c50, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42, c43, c43, c44, c44, c45, c45, c46, c46, c49, c49

389.10/118.85
389.10/118.85

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

Use narrowing to replace TOP(ok(z0)) → c50(TOP(active(z0)), ACTIVE(z0)) by

TOP(ok(U11(tt, z0))) → c50(TOP(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 389.10/118.85
TOP(ok(U12(tt))) → c50(TOP(mark(tt)), ACTIVE(U12(tt))) 389.10/118.85
TOP(ok(U21(tt))) → c50(TOP(mark(tt)), ACTIVE(U21(tt))) 389.10/118.85
TOP(ok(U31(tt, z0))) → c50(TOP(mark(z0)), ACTIVE(U31(tt, z0))) 389.10/118.85
TOP(ok(U41(tt, z0, z1))) → c50(TOP(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 389.10/118.85
TOP(ok(U42(tt, z0, z1))) → c50(TOP(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 389.10/118.85
TOP(ok(isNat(0))) → c50(TOP(mark(tt)), ACTIVE(isNat(0))) 389.10/118.85
TOP(ok(isNat(plus(z0, z1)))) → c50(TOP(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
TOP(ok(isNat(s(z0)))) → c50(TOP(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 389.10/118.85
TOP(ok(plus(z0, 0))) → c50(TOP(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
TOP(ok(plus(z0, s(z1)))) → c50(TOP(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
TOP(ok(U11(z0, z1))) → c50(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
TOP(ok(U12(z0))) → c50(TOP(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
TOP(ok(U21(z0))) → c50(TOP(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
TOP(ok(U31(z0, z1))) → c50(TOP(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
TOP(ok(U41(z0, z1, z2))) → c50(TOP(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
TOP(ok(U42(z0, z1, z2))) → c50(TOP(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
TOP(ok(s(z0))) → c50(TOP(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
TOP(ok(plus(z0, z1))) → c50(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
TOP(ok(plus(z0, z1))) → c50(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
389.10/118.85
389.10/118.85

(90) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.85
active(U12(tt)) → mark(tt) 389.10/118.85
active(U21(tt)) → mark(tt) 389.10/118.85
active(U31(tt, z0)) → mark(z0) 389.10/118.85
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.85
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.85
active(isNat(0)) → mark(tt) 389.10/118.85
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.85
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.85
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.85
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.85
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.85
active(U12(z0)) → U12(active(z0)) 389.10/118.85
active(U21(z0)) → U21(active(z0)) 389.10/118.85
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.85
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.85
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.85
active(s(z0)) → s(active(z0)) 389.10/118.85
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.85
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.85
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.85
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.85
U12(mark(z0)) → mark(U12(z0)) 389.10/118.85
U12(ok(z0)) → ok(U12(z0)) 389.10/118.85
U21(mark(z0)) → mark(U21(z0)) 389.10/118.85
U21(ok(z0)) → ok(U21(z0)) 389.10/118.85
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.85
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.85
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.85
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.85
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.85
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.85
s(mark(z0)) → mark(s(z0)) 389.10/118.85
s(ok(z0)) → ok(s(z0)) 389.10/118.85
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.85
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.85
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.85
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.85
proper(tt) → ok(tt) 389.10/118.85
proper(U12(z0)) → U12(proper(z0)) 389.10/118.85
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.85
proper(U21(z0)) → U21(proper(z0)) 389.10/118.85
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.85
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.85
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.85
proper(s(z0)) → s(proper(z0)) 389.10/118.85
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.85
proper(0) → ok(0) 389.10/118.85
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.85
top(mark(z0)) → top(proper(z0)) 389.10/118.85
top(ok(z0)) → top(active(z0))
Tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.85
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.85
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.85
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.85
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.85
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.85
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.85
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.85
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.85
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.85
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.85
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.85
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.85
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.85
S(mark(z0)) → c32(S(z0)) 389.10/118.85
S(ok(z0)) → c33(S(z0)) 389.10/118.85
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.85
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.85
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.85
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.85
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.85
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.85
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.85
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.85
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.85
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.85
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.85
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.85
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.85
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.85
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.85
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.85
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.85
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.85
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.85
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.85
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.85
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.85
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.85
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.85
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.85
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.85
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.85
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.85
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.85
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.85
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.85
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.85
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.85
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.85
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.85
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.85
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.85
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.85
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.85
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.85
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.85
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.85
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.85
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.85
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.85
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.85
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.85
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.85
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.85
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.85
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.85
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.85
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.85
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.85
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.85
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.85
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.85
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.85
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.85
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.85
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.85
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.85
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.85
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.85
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.85
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.85
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.85
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.85
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.85
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.85
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.85
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.85
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.85
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.85
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.85
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.85
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.85
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.85
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.85
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.85
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.85
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.85
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.85
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.85
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.85
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.85
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.85
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.85
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.85
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.85
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.85
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.85
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.85
PROPER(s(0)) → c45(S(ok(0))) 389.10/118.85
PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.85
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.85
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.85
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.85
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.85
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0)) 389.10/118.85
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(x1)) 389.10/118.85
TOP(mark(U11(z0, z1))) → c49(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
TOP(mark(U12(z0))) → c49(TOP(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
TOP(mark(isNat(z0))) → c49(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
TOP(mark(U21(z0))) → c49(TOP(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
TOP(mark(U31(z0, z1))) → c49(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
TOP(mark(U41(z0, z1, z2))) → c49(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
TOP(mark(U42(z0, z1, z2))) → c49(TOP(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
TOP(mark(s(z0))) → c49(TOP(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
TOP(mark(plus(z0, z1))) → c49(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
TOP(mark(tt)) → c49(TOP(ok(tt))) 389.10/118.85
TOP(mark(0)) → c49(TOP(ok(0))) 389.10/118.85
TOP(ok(U11(tt, z0))) → c50(TOP(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 389.10/118.85
TOP(ok(U12(tt))) → c50(TOP(mark(tt)), ACTIVE(U12(tt))) 389.10/118.85
TOP(ok(U21(tt))) → c50(TOP(mark(tt)), ACTIVE(U21(tt))) 389.10/118.85
TOP(ok(U31(tt, z0))) → c50(TOP(mark(z0)), ACTIVE(U31(tt, z0))) 389.10/118.85
TOP(ok(U41(tt, z0, z1))) → c50(TOP(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 389.10/118.85
TOP(ok(U42(tt, z0, z1))) → c50(TOP(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 389.10/118.85
TOP(ok(isNat(0))) → c50(TOP(mark(tt)), ACTIVE(isNat(0))) 389.10/118.85
TOP(ok(isNat(plus(z0, z1)))) → c50(TOP(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
TOP(ok(isNat(s(z0)))) → c50(TOP(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 389.10/118.85
TOP(ok(plus(z0, 0))) → c50(TOP(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
TOP(ok(plus(z0, s(z1)))) → c50(TOP(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
TOP(ok(U11(z0, z1))) → c50(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
TOP(ok(U12(z0))) → c50(TOP(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
TOP(ok(U21(z0))) → c50(TOP(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
TOP(ok(U31(z0, z1))) → c50(TOP(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
TOP(ok(U41(z0, z1, z2))) → c50(TOP(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
TOP(ok(U42(z0, z1, z2))) → c50(TOP(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
TOP(ok(s(z0))) → c50(TOP(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
TOP(ok(plus(z0, z1))) → c50(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
TOP(ok(plus(z0, z1))) → c50(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
S tuples:

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.85
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.85
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.85
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.85
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.85
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.85
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.85
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.85
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.85
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.85
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.85
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.85
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.85
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.85
S(mark(z0)) → c32(S(z0)) 389.10/118.85
S(ok(z0)) → c33(S(z0)) 389.10/118.85
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.85
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.85
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.85
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.85
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.85
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.85
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.85
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.85
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.85
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.85
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.85
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.85
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.85
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.85
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.85
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.85
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.85
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.85
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.85
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.85
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.85
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.85
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.85
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.85
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.85
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.85
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.85
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.85
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.85
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.85
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.85
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.85
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.85
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.85
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.85
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.85
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.85
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.85
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.85
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.85
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.85
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.85
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.85
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.85
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.85
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.85
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.85
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.85
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.85
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.85
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.85
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.85
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.85
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.85
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.85
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.85
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.85
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.85
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.85
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.85
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.85
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.85
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.85
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.85
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.85
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.85
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.85
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.85
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.85
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.85
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.85
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.85
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.85
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.85
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.85
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.85
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.85
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.85
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.85
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.85
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.85
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.85
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.85
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.85
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.85
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.85
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.85
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.85
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.85
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.85
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.85
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.85
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.85
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.85
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.85
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.85
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.85
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.85
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.85
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.85
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.85
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.85
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.85
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.85
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.85
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.85
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.85
PROPER(s(0)) → c45(S(ok(0))) 389.10/118.85
PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.85
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.85
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.85
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.85
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.85
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.85
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.85
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.85
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.85
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.85
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.85
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.85
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.85
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0)) 389.10/118.85
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.85
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(x1)) 389.10/118.85
TOP(mark(U11(z0, z1))) → c49(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.85
TOP(mark(U12(z0))) → c49(TOP(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.85
TOP(mark(isNat(z0))) → c49(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.85
TOP(mark(U21(z0))) → c49(TOP(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.85
TOP(mark(U31(z0, z1))) → c49(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.85
TOP(mark(U41(z0, z1, z2))) → c49(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.85
TOP(mark(U42(z0, z1, z2))) → c49(TOP(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.85
TOP(mark(s(z0))) → c49(TOP(s(proper(z0))), PROPER(s(z0))) 389.10/118.85
TOP(mark(plus(z0, z1))) → c49(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.85
TOP(mark(tt)) → c49(TOP(ok(tt))) 389.10/118.85
TOP(mark(0)) → c49(TOP(ok(0))) 389.10/118.85
TOP(ok(U11(tt, z0))) → c50(TOP(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 389.10/118.85
TOP(ok(U12(tt))) → c50(TOP(mark(tt)), ACTIVE(U12(tt))) 389.10/118.85
TOP(ok(U21(tt))) → c50(TOP(mark(tt)), ACTIVE(U21(tt))) 389.10/118.85
TOP(ok(U31(tt, z0))) → c50(TOP(mark(z0)), ACTIVE(U31(tt, z0))) 389.10/118.85
TOP(ok(U41(tt, z0, z1))) → c50(TOP(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 389.10/118.85
TOP(ok(U42(tt, z0, z1))) → c50(TOP(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 389.10/118.85
TOP(ok(isNat(0))) → c50(TOP(mark(tt)), ACTIVE(isNat(0))) 389.10/118.85
TOP(ok(isNat(plus(z0, z1)))) → c50(TOP(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 389.10/118.85
TOP(ok(isNat(s(z0)))) → c50(TOP(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 389.10/118.85
TOP(ok(plus(z0, 0))) → c50(TOP(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.85
TOP(ok(plus(z0, s(z1)))) → c50(TOP(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.85
TOP(ok(U11(z0, z1))) → c50(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.85
TOP(ok(U12(z0))) → c50(TOP(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.85
TOP(ok(U21(z0))) → c50(TOP(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.85
TOP(ok(U31(z0, z1))) → c50(TOP(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.85
TOP(ok(U41(z0, z1, z2))) → c50(TOP(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.85
TOP(ok(U42(z0, z1, z2))) → c50(TOP(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.85
TOP(ok(s(z0))) → c50(TOP(s(active(z0))), ACTIVE(s(z0))) 389.10/118.85
TOP(ok(plus(z0, z1))) → c50(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.85
TOP(ok(plus(z0, z1))) → c50(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

ACTIVE, U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT, PROPER, TOP

Compound Symbols:

c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48, c8, c10, c1, c11, c11, c, c12, c12, c2, c13, c13, c3, c14, c14, c4, c15, c15, c5, c16, c16, c6, c17, c17, c7, c37, c37, c39, c39, c40, c40, c41, c41, c42, c42, c43, c43, c44, c44, c45, c45, c46, c46, c49, c49, c50

389.10/118.86
389.10/118.86

(91) CdtUnreachableProof (EQUIVALENT transformation)

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

ACTIVE(plus(z0, z1)) → c18(PLUS(active(z0), z1), ACTIVE(z0)) 389.10/118.86
ACTIVE(plus(z0, z1)) → c19(PLUS(z0, active(z1)), ACTIVE(z1)) 389.10/118.86
ACTIVE(isNat(s(z0))) → c8(ISNAT(z0)) 389.10/118.86
ACTIVE(plus(z0, s(z1))) → c10(ISNAT(z1)) 389.10/118.86
ACTIVE(U11(tt, z0)) → c1(U12'(isNat(z0))) 389.10/118.86
ACTIVE(U11(tt, z0)) → c1(ISNAT(z0)) 389.10/118.86
ACTIVE(U41(tt, z0, z1)) → c1(U42'(isNat(z1), z0, z1)) 389.10/118.86
ACTIVE(U41(tt, z0, z1)) → c1(ISNAT(z1)) 389.10/118.86
ACTIVE(U42(tt, z0, z1)) → c1(S(plus(z1, z0))) 389.10/118.86
ACTIVE(U42(tt, z0, z1)) → c1(PLUS(z1, z0)) 389.10/118.86
ACTIVE(isNat(plus(z0, z1))) → c1(U11'(isNat(z0), z1)) 389.10/118.86
ACTIVE(isNat(plus(z0, z1))) → c1(ISNAT(z0)) 389.10/118.86
ACTIVE(plus(z0, 0)) → c1(U31'(isNat(z0), z0)) 389.10/118.86
ACTIVE(plus(z0, 0)) → c1(ISNAT(z0)) 389.10/118.86
ACTIVE(U11(plus(z0, 0), x1)) → c11(U11'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.86
ACTIVE(U11(plus(z0, s(z1)), x1)) → c11(U11'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.86
ACTIVE(U11(U11(z0, z1), x1)) → c11(U11'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.86
ACTIVE(U11(U12(z0), x1)) → c11(U11'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.86
ACTIVE(U11(U21(z0), x1)) → c11(U11'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.86
ACTIVE(U11(U31(z0, z1), x1)) → c11(U11'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.86
ACTIVE(U11(U41(z0, z1, z2), x1)) → c11(U11'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.86
ACTIVE(U11(U42(z0, z1, z2), x1)) → c11(U11'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.86
ACTIVE(U11(s(z0), x1)) → c11(U11'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.86
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U11(plus(z0, z1), x1)) → c11(U11'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U11(isNat(0), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.86
ACTIVE(U11(U11(tt, z0), x1)) → c(U11'(mark(U12(isNat(z0))), x1)) 389.10/118.86
ACTIVE(U11(U11(tt, z0), x1)) → c(ACTIVE(U11(tt, z0))) 389.10/118.86
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(U11'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.86
ACTIVE(U11(isNat(plus(z0, z1)), x1)) → c(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.86
ACTIVE(U11(isNat(s(z0)), x1)) → c(U11'(mark(U21(isNat(z0))), x1)) 389.10/118.86
ACTIVE(U11(isNat(s(z0)), x1)) → c(ACTIVE(isNat(s(z0)))) 389.10/118.86
ACTIVE(U12(plus(z0, 0))) → c12(U12'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.86
ACTIVE(U12(plus(z0, s(z1)))) → c12(U12'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.86
ACTIVE(U12(U11(z0, z1))) → c12(U12'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.86
ACTIVE(U12(U12(z0))) → c12(U12'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.86
ACTIVE(U12(U21(z0))) → c12(U12'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.86
ACTIVE(U12(U31(z0, z1))) → c12(U12'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.86
ACTIVE(U12(U41(z0, z1, z2))) → c12(U12'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.86
ACTIVE(U12(U42(z0, z1, z2))) → c12(U12'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.86
ACTIVE(U12(s(z0))) → c12(U12'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.86
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U12(plus(z0, z1))) → c12(U12'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U11(U12(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.86
ACTIVE(U12(U12(tt))) → c12(U12'(mark(tt))) 389.10/118.86
ACTIVE(U12(isNat(0))) → c12(U12'(mark(tt))) 389.10/118.86
ACTIVE(U12(U11(tt, z0))) → c2(U12'(mark(U12(isNat(z0))))) 389.10/118.86
ACTIVE(U12(U11(tt, z0))) → c2(ACTIVE(U11(tt, z0))) 389.10/118.86
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(U12'(mark(U11(isNat(z0), z1)))) 389.10/118.86
ACTIVE(U12(isNat(plus(z0, z1)))) → c2(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.86
ACTIVE(U12(isNat(s(z0)))) → c2(U12'(mark(U21(isNat(z0))))) 389.10/118.86
ACTIVE(U12(isNat(s(z0)))) → c2(ACTIVE(isNat(s(z0)))) 389.10/118.86
ACTIVE(U21(plus(z0, 0))) → c13(U21'(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.86
ACTIVE(U21(plus(z0, s(z1)))) → c13(U21'(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.86
ACTIVE(U21(U11(z0, z1))) → c13(U21'(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.86
ACTIVE(U21(U12(z0))) → c13(U21'(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.86
ACTIVE(U21(U21(z0))) → c13(U21'(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.86
ACTIVE(U21(U31(z0, z1))) → c13(U21'(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.86
ACTIVE(U21(U41(z0, z1, z2))) → c13(U21'(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.86
ACTIVE(U21(U42(z0, z1, z2))) → c13(U21'(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.86
ACTIVE(U21(s(z0))) → c13(U21'(s(active(z0))), ACTIVE(s(z0))) 389.10/118.86
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U21(plus(z0, z1))) → c13(U21'(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U11(U21(tt), x1)) → c11(U11'(mark(tt), x1)) 389.10/118.86
ACTIVE(U12(U21(tt))) → c12(U12'(mark(tt))) 389.10/118.86
ACTIVE(U21(U12(tt))) → c13(U21'(mark(tt))) 389.10/118.86
ACTIVE(U21(U21(tt))) → c13(U21'(mark(tt))) 389.10/118.86
ACTIVE(U21(isNat(0))) → c13(U21'(mark(tt))) 389.10/118.86
ACTIVE(U21(U11(tt, z0))) → c3(U21'(mark(U12(isNat(z0))))) 389.10/118.86
ACTIVE(U21(U11(tt, z0))) → c3(ACTIVE(U11(tt, z0))) 389.10/118.86
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(U21'(mark(U11(isNat(z0), z1)))) 389.10/118.86
ACTIVE(U21(isNat(plus(z0, z1)))) → c3(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.86
ACTIVE(U21(isNat(s(z0)))) → c3(U21'(mark(U21(isNat(z0))))) 389.10/118.86
ACTIVE(U21(isNat(s(z0)))) → c3(ACTIVE(isNat(s(z0)))) 389.10/118.86
ACTIVE(U31(plus(z0, 0), x1)) → c14(U31'(mark(U31(isNat(z0), z0)), x1), ACTIVE(plus(z0, 0))) 389.10/118.86
ACTIVE(U31(plus(z0, s(z1)), x1)) → c14(U31'(mark(U41(isNat(z1), z1, z0)), x1), ACTIVE(plus(z0, s(z1)))) 389.10/118.86
ACTIVE(U31(U11(z0, z1), x1)) → c14(U31'(U11(active(z0), z1), x1), ACTIVE(U11(z0, z1))) 389.10/118.86
ACTIVE(U31(U12(z0), x1)) → c14(U31'(U12(active(z0)), x1), ACTIVE(U12(z0))) 389.10/118.86
ACTIVE(U31(U21(z0), x1)) → c14(U31'(U21(active(z0)), x1), ACTIVE(U21(z0))) 389.10/118.86
ACTIVE(U31(U31(z0, z1), x1)) → c14(U31'(U31(active(z0), z1), x1), ACTIVE(U31(z0, z1))) 389.10/118.86
ACTIVE(U31(U41(z0, z1, z2), x1)) → c14(U31'(U41(active(z0), z1, z2), x1), ACTIVE(U41(z0, z1, z2))) 389.10/118.86
ACTIVE(U31(U42(z0, z1, z2), x1)) → c14(U31'(U42(active(z0), z1, z2), x1), ACTIVE(U42(z0, z1, z2))) 389.10/118.86
ACTIVE(U31(s(z0), x1)) → c14(U31'(s(active(z0)), x1), ACTIVE(s(z0))) 389.10/118.86
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(active(z0), z1), x1), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U31(plus(z0, z1), x1)) → c14(U31'(plus(z0, active(z1)), x1), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U11(U31(tt, z0), x1)) → c11(U11'(mark(z0), x1)) 389.10/118.86
ACTIVE(U12(U31(tt, z0))) → c12(U12'(mark(z0))) 389.10/118.86
ACTIVE(U21(U31(tt, z0))) → c13(U21'(mark(z0))) 389.10/118.86
ACTIVE(U31(U12(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.86
ACTIVE(U31(U21(tt), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.86
ACTIVE(U31(U31(tt, z0), x1)) → c14(U31'(mark(z0), x1)) 389.10/118.86
ACTIVE(U31(isNat(0), x1)) → c14(U31'(mark(tt), x1)) 389.10/118.86
ACTIVE(U31(U11(tt, z0), x1)) → c4(U31'(mark(U12(isNat(z0))), x1)) 389.10/118.86
ACTIVE(U31(U11(tt, z0), x1)) → c4(ACTIVE(U11(tt, z0))) 389.10/118.86
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(U31'(mark(U11(isNat(z0), z1)), x1)) 389.10/118.86
ACTIVE(U31(isNat(plus(z0, z1)), x1)) → c4(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.86
ACTIVE(U31(isNat(s(z0)), x1)) → c4(U31'(mark(U21(isNat(z0))), x1)) 389.10/118.86
ACTIVE(U31(isNat(s(z0)), x1)) → c4(ACTIVE(isNat(s(z0)))) 389.10/118.86
ACTIVE(U41(plus(z0, 0), x1, x2)) → c15(U41'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.86
ACTIVE(U41(plus(z0, s(z1)), x1, x2)) → c15(U41'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.86
ACTIVE(U41(U11(z0, z1), x1, x2)) → c15(U41'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.86
ACTIVE(U41(U12(z0), x1, x2)) → c15(U41'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.86
ACTIVE(U41(U21(z0), x1, x2)) → c15(U41'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.86
ACTIVE(U41(U31(z0, z1), x1, x2)) → c15(U41'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.86
ACTIVE(U41(U41(z0, z1, z2), x1, x2)) → c15(U41'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.86
ACTIVE(U41(U42(z0, z1, z2), x1, x2)) → c15(U41'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.86
ACTIVE(U41(s(z0), x1, x2)) → c15(U41'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.86
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U41(plus(z0, z1), x1, x2)) → c15(U41'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U41(U12(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.86
ACTIVE(U41(U21(tt), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.86
ACTIVE(U41(U31(tt, z0), x1, x2)) → c15(U41'(mark(z0), x1, x2)) 389.10/118.86
ACTIVE(U41(isNat(0), x1, x2)) → c15(U41'(mark(tt), x1, x2)) 389.10/118.86
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(U11'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.86
ACTIVE(U11(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.86
ACTIVE(U12(U41(tt, z0, z1))) → c5(U12'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.86
ACTIVE(U12(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.86
ACTIVE(U21(U41(tt, z0, z1))) → c5(U21'(mark(U42(isNat(z1), z0, z1)))) 389.10/118.86
ACTIVE(U21(U41(tt, z0, z1))) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.86
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(U31'(mark(U42(isNat(z1), z0, z1)), x1)) 389.10/118.86
ACTIVE(U31(U41(tt, z0, z1), x1)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.86
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(U41'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.86
ACTIVE(U41(U11(tt, z0), x1, x2)) → c5(ACTIVE(U11(tt, z0))) 389.10/118.86
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(U41'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.86
ACTIVE(U41(U41(tt, z0, z1), x1, x2)) → c5(ACTIVE(U41(tt, z0, z1))) 389.10/118.86
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(U41'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.86
ACTIVE(U41(isNat(plus(z0, z1)), x1, x2)) → c5(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.86
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(U41'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.86
ACTIVE(U41(isNat(s(z0)), x1, x2)) → c5(ACTIVE(isNat(s(z0)))) 389.10/118.86
ACTIVE(U42(plus(z0, 0), x1, x2)) → c16(U42'(mark(U31(isNat(z0), z0)), x1, x2), ACTIVE(plus(z0, 0))) 389.10/118.86
ACTIVE(U42(plus(z0, s(z1)), x1, x2)) → c16(U42'(mark(U41(isNat(z1), z1, z0)), x1, x2), ACTIVE(plus(z0, s(z1)))) 389.10/118.86
ACTIVE(U42(U11(z0, z1), x1, x2)) → c16(U42'(U11(active(z0), z1), x1, x2), ACTIVE(U11(z0, z1))) 389.10/118.86
ACTIVE(U42(U12(z0), x1, x2)) → c16(U42'(U12(active(z0)), x1, x2), ACTIVE(U12(z0))) 389.10/118.86
ACTIVE(U42(U21(z0), x1, x2)) → c16(U42'(U21(active(z0)), x1, x2), ACTIVE(U21(z0))) 389.10/118.86
ACTIVE(U42(U31(z0, z1), x1, x2)) → c16(U42'(U31(active(z0), z1), x1, x2), ACTIVE(U31(z0, z1))) 389.10/118.86
ACTIVE(U42(U41(z0, z1, z2), x1, x2)) → c16(U42'(U41(active(z0), z1, z2), x1, x2), ACTIVE(U41(z0, z1, z2))) 389.10/118.86
ACTIVE(U42(U42(z0, z1, z2), x1, x2)) → c16(U42'(U42(active(z0), z1, z2), x1, x2), ACTIVE(U42(z0, z1, z2))) 389.10/118.86
ACTIVE(U42(s(z0), x1, x2)) → c16(U42'(s(active(z0)), x1, x2), ACTIVE(s(z0))) 389.10/118.86
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(active(z0), z1), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U42(plus(z0, z1), x1, x2)) → c16(U42'(plus(z0, active(z1)), x1, x2), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(U42(U12(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.86
ACTIVE(U42(U21(tt), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.86
ACTIVE(U42(U31(tt, z0), x1, x2)) → c16(U42'(mark(z0), x1, x2)) 389.10/118.86
ACTIVE(U42(isNat(0), x1, x2)) → c16(U42'(mark(tt), x1, x2)) 389.10/118.86
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(U11'(mark(s(plus(z1, z0))), x1)) 389.10/118.86
ACTIVE(U11(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.86
ACTIVE(U12(U42(tt, z0, z1))) → c6(U12'(mark(s(plus(z1, z0))))) 389.10/118.86
ACTIVE(U12(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.86
ACTIVE(U21(U42(tt, z0, z1))) → c6(U21'(mark(s(plus(z1, z0))))) 389.10/118.86
ACTIVE(U21(U42(tt, z0, z1))) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.86
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(U31'(mark(s(plus(z1, z0))), x1)) 389.10/118.86
ACTIVE(U31(U42(tt, z0, z1), x1)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.86
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(U41'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.86
ACTIVE(U41(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.86
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(U42'(mark(U12(isNat(z0))), x1, x2)) 389.10/118.86
ACTIVE(U42(U11(tt, z0), x1, x2)) → c6(ACTIVE(U11(tt, z0))) 389.10/118.86
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(U42'(mark(U42(isNat(z1), z0, z1)), x1, x2)) 389.10/118.86
ACTIVE(U42(U41(tt, z0, z1), x1, x2)) → c6(ACTIVE(U41(tt, z0, z1))) 389.10/118.86
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(U42'(mark(s(plus(z1, z0))), x1, x2)) 389.10/118.86
ACTIVE(U42(U42(tt, z0, z1), x1, x2)) → c6(ACTIVE(U42(tt, z0, z1))) 389.10/118.86
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(U42'(mark(U11(isNat(z0), z1)), x1, x2)) 389.10/118.86
ACTIVE(U42(isNat(plus(z0, z1)), x1, x2)) → c6(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.86
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(U42'(mark(U21(isNat(z0))), x1, x2)) 389.10/118.86
ACTIVE(U42(isNat(s(z0)), x1, x2)) → c6(ACTIVE(isNat(s(z0)))) 389.10/118.86
ACTIVE(s(plus(z0, 0))) → c17(S(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.86
ACTIVE(s(plus(z0, s(z1)))) → c17(S(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.86
ACTIVE(s(U11(z0, z1))) → c17(S(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.86
ACTIVE(s(U12(z0))) → c17(S(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.86
ACTIVE(s(U21(z0))) → c17(S(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.86
ACTIVE(s(U31(z0, z1))) → c17(S(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.86
ACTIVE(s(U41(z0, z1, z2))) → c17(S(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.86
ACTIVE(s(U42(z0, z1, z2))) → c17(S(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.86
ACTIVE(s(s(z0))) → c17(S(s(active(z0))), ACTIVE(s(z0))) 389.10/118.86
ACTIVE(s(plus(z0, z1))) → c17(S(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(s(plus(z0, z1))) → c17(S(plus(z0, active(z1))), ACTIVE(plus(z0, z1))) 389.10/118.86
ACTIVE(s(U12(tt))) → c17(S(mark(tt))) 389.10/118.86
ACTIVE(s(U21(tt))) → c17(S(mark(tt))) 389.10/118.86
ACTIVE(s(U31(tt, z0))) → c17(S(mark(z0))) 389.10/118.86
ACTIVE(s(isNat(0))) → c17(S(mark(tt))) 389.10/118.86
ACTIVE(s(U11(tt, z0))) → c7(S(mark(U12(isNat(z0))))) 389.10/118.86
ACTIVE(s(U11(tt, z0))) → c7(ACTIVE(U11(tt, z0))) 389.10/118.86
ACTIVE(s(U41(tt, z0, z1))) → c7(S(mark(U42(isNat(z1), z0, z1)))) 389.10/118.86
ACTIVE(s(U41(tt, z0, z1))) → c7(ACTIVE(U41(tt, z0, z1))) 389.10/118.86
ACTIVE(s(U42(tt, z0, z1))) → c7(S(mark(s(plus(z1, z0))))) 389.10/118.86
ACTIVE(s(U42(tt, z0, z1))) → c7(ACTIVE(U42(tt, z0, z1))) 389.10/118.86
ACTIVE(s(isNat(plus(z0, z1)))) → c7(S(mark(U11(isNat(z0), z1)))) 389.10/118.86
ACTIVE(s(isNat(plus(z0, z1)))) → c7(ACTIVE(isNat(plus(z0, z1)))) 389.10/118.86
ACTIVE(s(isNat(s(z0)))) → c7(S(mark(U21(isNat(z0))))) 389.10/118.86
ACTIVE(s(isNat(s(z0)))) → c7(ACTIVE(isNat(s(z0)))) 389.10/118.86
PROPER(U11(x0, U11(z0, z1))) → c37(U11'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.86
PROPER(U11(x0, U12(z0))) → c37(U11'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.86
PROPER(U11(x0, isNat(z0))) → c37(U11'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.86
PROPER(U11(x0, U21(z0))) → c37(U11'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.86
PROPER(U11(x0, U31(z0, z1))) → c37(U11'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.86
PROPER(U11(x0, U41(z0, z1, z2))) → c37(U11'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.86
PROPER(U11(x0, U42(z0, z1, z2))) → c37(U11'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.86
PROPER(U11(x0, s(z0))) → c37(U11'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.86
PROPER(U11(x0, plus(z0, z1))) → c37(U11'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.86
PROPER(U11(U11(z0, z1), x1)) → c37(U11'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.86
PROPER(U11(U12(z0), x1)) → c37(U11'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.86
PROPER(U11(isNat(z0), x1)) → c37(U11'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.86
PROPER(U11(U21(z0), x1)) → c37(U11'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.86
PROPER(U11(U31(z0, z1), x1)) → c37(U11'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.86
PROPER(U11(U41(z0, z1, z2), x1)) → c37(U11'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.86
PROPER(U11(U42(z0, z1, z2), x1)) → c37(U11'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.86
PROPER(U11(s(z0), x1)) → c37(U11'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.86
PROPER(U11(plus(z0, z1), x1)) → c37(U11'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.86
PROPER(U11(x0, tt)) → c37(U11'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.86
PROPER(U11(x0, 0)) → c37(U11'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.86
PROPER(U11(tt, x1)) → c37(U11'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.86
PROPER(U11(0, x1)) → c37(U11'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.86
PROPER(U12(U11(z0, z1))) → c39(U12'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.86
PROPER(U12(U12(z0))) → c39(U12'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.86
PROPER(U12(isNat(z0))) → c39(U12'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.86
PROPER(U12(U21(z0))) → c39(U12'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.86
PROPER(U12(U31(z0, z1))) → c39(U12'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.86
PROPER(U12(U41(z0, z1, z2))) → c39(U12'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.86
PROPER(U12(U42(z0, z1, z2))) → c39(U12'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.86
PROPER(U12(s(z0))) → c39(U12'(s(proper(z0))), PROPER(s(z0))) 389.10/118.86
PROPER(U12(plus(z0, z1))) → c39(U12'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.86
PROPER(U12(tt)) → c39(U12'(ok(tt))) 389.10/118.86
PROPER(U12(0)) → c39(U12'(ok(0))) 389.10/118.86
PROPER(isNat(U11(z0, z1))) → c40(ISNAT(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.86
PROPER(isNat(U12(z0))) → c40(ISNAT(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.86
PROPER(isNat(isNat(z0))) → c40(ISNAT(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.86
PROPER(isNat(U21(z0))) → c40(ISNAT(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.86
PROPER(isNat(U31(z0, z1))) → c40(ISNAT(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.86
PROPER(isNat(U41(z0, z1, z2))) → c40(ISNAT(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.86
PROPER(isNat(U42(z0, z1, z2))) → c40(ISNAT(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.86
PROPER(isNat(s(z0))) → c40(ISNAT(s(proper(z0))), PROPER(s(z0))) 389.10/118.86
PROPER(isNat(plus(z0, z1))) → c40(ISNAT(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.86
PROPER(isNat(tt)) → c40(ISNAT(ok(tt))) 389.10/118.86
PROPER(isNat(0)) → c40(ISNAT(ok(0))) 389.10/118.86
PROPER(U21(U11(z0, z1))) → c41(U21'(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.86
PROPER(U21(U12(z0))) → c41(U21'(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.86
PROPER(U21(isNat(z0))) → c41(U21'(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.86
PROPER(U21(U21(z0))) → c41(U21'(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.86
PROPER(U21(U31(z0, z1))) → c41(U21'(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.86
PROPER(U21(U41(z0, z1, z2))) → c41(U21'(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.86
PROPER(U21(U42(z0, z1, z2))) → c41(U21'(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.86
PROPER(U21(s(z0))) → c41(U21'(s(proper(z0))), PROPER(s(z0))) 389.10/118.86
PROPER(U21(plus(z0, z1))) → c41(U21'(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.86
PROPER(U21(tt)) → c41(U21'(ok(tt))) 389.10/118.86
PROPER(U21(0)) → c41(U21'(ok(0))) 389.10/118.86
PROPER(U31(x0, U11(z0, z1))) → c42(U31'(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.86
PROPER(U31(x0, U12(z0))) → c42(U31'(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.86
PROPER(U31(x0, isNat(z0))) → c42(U31'(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.86
PROPER(U31(x0, U21(z0))) → c42(U31'(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.86
PROPER(U31(x0, U31(z0, z1))) → c42(U31'(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.86
PROPER(U31(x0, U41(z0, z1, z2))) → c42(U31'(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.86
PROPER(U31(x0, U42(z0, z1, z2))) → c42(U31'(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.86
PROPER(U31(x0, s(z0))) → c42(U31'(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.86
PROPER(U31(x0, plus(z0, z1))) → c42(U31'(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.86
PROPER(U31(U11(z0, z1), x1)) → c42(U31'(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.86
PROPER(U31(U12(z0), x1)) → c42(U31'(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.86
PROPER(U31(isNat(z0), x1)) → c42(U31'(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.86
PROPER(U31(U21(z0), x1)) → c42(U31'(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.86
PROPER(U31(U31(z0, z1), x1)) → c42(U31'(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.86
PROPER(U31(U41(z0, z1, z2), x1)) → c42(U31'(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.86
PROPER(U31(U42(z0, z1, z2), x1)) → c42(U31'(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.86
PROPER(U31(s(z0), x1)) → c42(U31'(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.86
PROPER(U31(plus(z0, z1), x1)) → c42(U31'(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.86
PROPER(U31(x0, tt)) → c42(U31'(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.86
PROPER(U31(x0, 0)) → c42(U31'(proper(x0), ok(0)), PROPER(x0)) 389.10/118.86
PROPER(U31(tt, x1)) → c42(U31'(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.86
PROPER(U31(0, x1)) → c42(U31'(ok(0), proper(x1)), PROPER(x1)) 389.10/118.86
PROPER(U41(x0, x1, U11(z0, z1))) → c43(U41'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.86
PROPER(U41(x0, x1, U12(z0))) → c43(U41'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.86
PROPER(U41(x0, x1, isNat(z0))) → c43(U41'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.86
PROPER(U41(x0, x1, U21(z0))) → c43(U41'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.86
PROPER(U41(x0, x1, U31(z0, z1))) → c43(U41'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.86
PROPER(U41(x0, x1, U41(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.86
PROPER(U41(x0, x1, U42(z0, z1, z2))) → c43(U41'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.86
PROPER(U41(x0, x1, s(z0))) → c43(U41'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.86
PROPER(U41(x0, x1, plus(z0, z1))) → c43(U41'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.86
PROPER(U41(x0, U11(z0, z1), x2)) → c43(U41'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.86
PROPER(U41(x0, U12(z0), x2)) → c43(U41'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.86
PROPER(U41(x0, isNat(z0), x2)) → c43(U41'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.86
PROPER(U41(x0, U21(z0), x2)) → c43(U41'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.86
PROPER(U41(x0, U31(z0, z1), x2)) → c43(U41'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.86
PROPER(U41(x0, U41(z0, z1, z2), x2)) → c43(U41'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.86
PROPER(U41(x0, U42(z0, z1, z2), x2)) → c43(U41'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.86
PROPER(U41(x0, s(z0), x2)) → c43(U41'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.86
PROPER(U41(x0, plus(z0, z1), x2)) → c43(U41'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.86
PROPER(U41(U11(z0, z1), x1, x2)) → c43(U41'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U41(U12(z0), x1, x2)) → c43(U41'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U41(isNat(z0), x1, x2)) → c43(U41'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U41(U21(z0), x1, x2)) → c43(U41'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U41(U31(z0, z1), x1, x2)) → c43(U41'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U41(U41(z0, z1, z2), x1, x2)) → c43(U41'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U41(U42(z0, z1, z2), x1, x2)) → c43(U41'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U41(s(z0), x1, x2)) → c43(U41'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U41(plus(z0, z1), x1, x2)) → c43(U41'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U41(x0, x1, tt)) → c43(U41'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.86
PROPER(U41(x0, x1, 0)) → c43(U41'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.86
PROPER(U41(x0, tt, x2)) → c43(U41'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.86
PROPER(U41(x0, 0, x2)) → c43(U41'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.86
PROPER(U41(tt, x1, x2)) → c43(U41'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U41(0, x1, x2)) → c43(U41'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U42(x0, x1, U11(z0, z1))) → c44(U42'(proper(x0), proper(x1), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U11(z0, z1))) 389.10/118.86
PROPER(U42(x0, x1, U12(z0))) → c44(U42'(proper(x0), proper(x1), U12(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U12(z0))) 389.10/118.86
PROPER(U42(x0, x1, isNat(z0))) → c44(U42'(proper(x0), proper(x1), isNat(proper(z0))), PROPER(x0), PROPER(x1), PROPER(isNat(z0))) 389.10/118.86
PROPER(U42(x0, x1, U21(z0))) → c44(U42'(proper(x0), proper(x1), U21(proper(z0))), PROPER(x0), PROPER(x1), PROPER(U21(z0))) 389.10/118.86
PROPER(U42(x0, x1, U31(z0, z1))) → c44(U42'(proper(x0), proper(x1), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(U31(z0, z1))) 389.10/118.86
PROPER(U42(x0, x1, U41(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U41(z0, z1, z2))) 389.10/118.86
PROPER(U42(x0, x1, U42(z0, z1, z2))) → c44(U42'(proper(x0), proper(x1), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(x1), PROPER(U42(z0, z1, z2))) 389.10/118.86
PROPER(U42(x0, x1, s(z0))) → c44(U42'(proper(x0), proper(x1), s(proper(z0))), PROPER(x0), PROPER(x1), PROPER(s(z0))) 389.10/118.86
PROPER(U42(x0, x1, plus(z0, z1))) → c44(U42'(proper(x0), proper(x1), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(x1), PROPER(plus(z0, z1))) 389.10/118.86
PROPER(U42(x0, U11(z0, z1), x2)) → c44(U42'(proper(x0), U11(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U11(z0, z1)), PROPER(x2)) 389.10/118.86
PROPER(U42(x0, U12(z0), x2)) → c44(U42'(proper(x0), U12(proper(z0)), proper(x2)), PROPER(x0), PROPER(U12(z0)), PROPER(x2)) 389.10/118.86
PROPER(U42(x0, isNat(z0), x2)) → c44(U42'(proper(x0), isNat(proper(z0)), proper(x2)), PROPER(x0), PROPER(isNat(z0)), PROPER(x2)) 389.10/118.86
PROPER(U42(x0, U21(z0), x2)) → c44(U42'(proper(x0), U21(proper(z0)), proper(x2)), PROPER(x0), PROPER(U21(z0)), PROPER(x2)) 389.10/118.86
PROPER(U42(x0, U31(z0, z1), x2)) → c44(U42'(proper(x0), U31(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(U31(z0, z1)), PROPER(x2)) 389.10/118.86
PROPER(U42(x0, U41(z0, z1, z2), x2)) → c44(U42'(proper(x0), U41(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U41(z0, z1, z2)), PROPER(x2)) 389.10/118.86
PROPER(U42(x0, U42(z0, z1, z2), x2)) → c44(U42'(proper(x0), U42(proper(z0), proper(z1), proper(z2)), proper(x2)), PROPER(x0), PROPER(U42(z0, z1, z2)), PROPER(x2)) 389.10/118.86
PROPER(U42(x0, s(z0), x2)) → c44(U42'(proper(x0), s(proper(z0)), proper(x2)), PROPER(x0), PROPER(s(z0)), PROPER(x2)) 389.10/118.86
PROPER(U42(x0, plus(z0, z1), x2)) → c44(U42'(proper(x0), plus(proper(z0), proper(z1)), proper(x2)), PROPER(x0), PROPER(plus(z0, z1)), PROPER(x2)) 389.10/118.86
PROPER(U42(U11(z0, z1), x1, x2)) → c44(U42'(U11(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U11(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U42(U12(z0), x1, x2)) → c44(U42'(U12(proper(z0)), proper(x1), proper(x2)), PROPER(U12(z0)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U42(isNat(z0), x1, x2)) → c44(U42'(isNat(proper(z0)), proper(x1), proper(x2)), PROPER(isNat(z0)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U42(U21(z0), x1, x2)) → c44(U42'(U21(proper(z0)), proper(x1), proper(x2)), PROPER(U21(z0)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U42(U31(z0, z1), x1, x2)) → c44(U42'(U31(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(U31(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U42(U41(z0, z1, z2), x1, x2)) → c44(U42'(U41(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U41(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U42(U42(z0, z1, z2), x1, x2)) → c44(U42'(U42(proper(z0), proper(z1), proper(z2)), proper(x1), proper(x2)), PROPER(U42(z0, z1, z2)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U42(s(z0), x1, x2)) → c44(U42'(s(proper(z0)), proper(x1), proper(x2)), PROPER(s(z0)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U42(plus(z0, z1), x1, x2)) → c44(U42'(plus(proper(z0), proper(z1)), proper(x1), proper(x2)), PROPER(plus(z0, z1)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U42(x0, x1, tt)) → c44(U42'(proper(x0), proper(x1), ok(tt)), PROPER(x0), PROPER(x1)) 389.10/118.86
PROPER(U42(x0, x1, 0)) → c44(U42'(proper(x0), proper(x1), ok(0)), PROPER(x0), PROPER(x1)) 389.10/118.86
PROPER(U42(x0, tt, x2)) → c44(U42'(proper(x0), ok(tt), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.86
PROPER(U42(x0, 0, x2)) → c44(U42'(proper(x0), ok(0), proper(x2)), PROPER(x0), PROPER(x2)) 389.10/118.86
PROPER(U42(tt, x1, x2)) → c44(U42'(ok(tt), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(U42(0, x1, x2)) → c44(U42'(ok(0), proper(x1), proper(x2)), PROPER(x1), PROPER(x2)) 389.10/118.86
PROPER(s(U11(z0, z1))) → c45(S(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.86
PROPER(s(U12(z0))) → c45(S(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.86
PROPER(s(isNat(z0))) → c45(S(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.86
PROPER(s(U21(z0))) → c45(S(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.86
PROPER(s(U31(z0, z1))) → c45(S(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.86
PROPER(s(U41(z0, z1, z2))) → c45(S(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.86
PROPER(s(U42(z0, z1, z2))) → c45(S(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.86
PROPER(s(s(z0))) → c45(S(s(proper(z0))), PROPER(s(z0))) 389.10/118.86
PROPER(s(plus(z0, z1))) → c45(S(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.86
PROPER(s(tt)) → c45(S(ok(tt))) 389.10/118.86
PROPER(s(0)) → c45(S(ok(0))) 389.10/118.86
PROPER(plus(x0, U11(z0, z1))) → c46(PLUS(proper(x0), U11(proper(z0), proper(z1))), PROPER(x0), PROPER(U11(z0, z1))) 389.10/118.86
PROPER(plus(x0, U12(z0))) → c46(PLUS(proper(x0), U12(proper(z0))), PROPER(x0), PROPER(U12(z0))) 389.10/118.86
PROPER(plus(x0, isNat(z0))) → c46(PLUS(proper(x0), isNat(proper(z0))), PROPER(x0), PROPER(isNat(z0))) 389.10/118.86
PROPER(plus(x0, U21(z0))) → c46(PLUS(proper(x0), U21(proper(z0))), PROPER(x0), PROPER(U21(z0))) 389.10/118.86
PROPER(plus(x0, U31(z0, z1))) → c46(PLUS(proper(x0), U31(proper(z0), proper(z1))), PROPER(x0), PROPER(U31(z0, z1))) 389.10/118.86
PROPER(plus(x0, U41(z0, z1, z2))) → c46(PLUS(proper(x0), U41(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U41(z0, z1, z2))) 389.10/118.86
PROPER(plus(x0, U42(z0, z1, z2))) → c46(PLUS(proper(x0), U42(proper(z0), proper(z1), proper(z2))), PROPER(x0), PROPER(U42(z0, z1, z2))) 389.10/118.86
PROPER(plus(x0, s(z0))) → c46(PLUS(proper(x0), s(proper(z0))), PROPER(x0), PROPER(s(z0))) 389.10/118.86
PROPER(plus(x0, plus(z0, z1))) → c46(PLUS(proper(x0), plus(proper(z0), proper(z1))), PROPER(x0), PROPER(plus(z0, z1))) 389.10/118.86
PROPER(plus(U11(z0, z1), x1)) → c46(PLUS(U11(proper(z0), proper(z1)), proper(x1)), PROPER(U11(z0, z1)), PROPER(x1)) 389.10/118.86
PROPER(plus(U12(z0), x1)) → c46(PLUS(U12(proper(z0)), proper(x1)), PROPER(U12(z0)), PROPER(x1)) 389.10/118.86
PROPER(plus(isNat(z0), x1)) → c46(PLUS(isNat(proper(z0)), proper(x1)), PROPER(isNat(z0)), PROPER(x1)) 389.10/118.86
PROPER(plus(U21(z0), x1)) → c46(PLUS(U21(proper(z0)), proper(x1)), PROPER(U21(z0)), PROPER(x1)) 389.10/118.86
PROPER(plus(U31(z0, z1), x1)) → c46(PLUS(U31(proper(z0), proper(z1)), proper(x1)), PROPER(U31(z0, z1)), PROPER(x1)) 389.10/118.86
PROPER(plus(U41(z0, z1, z2), x1)) → c46(PLUS(U41(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U41(z0, z1, z2)), PROPER(x1)) 389.10/118.86
PROPER(plus(U42(z0, z1, z2), x1)) → c46(PLUS(U42(proper(z0), proper(z1), proper(z2)), proper(x1)), PROPER(U42(z0, z1, z2)), PROPER(x1)) 389.10/118.86
PROPER(plus(s(z0), x1)) → c46(PLUS(s(proper(z0)), proper(x1)), PROPER(s(z0)), PROPER(x1)) 389.10/118.86
PROPER(plus(plus(z0, z1), x1)) → c46(PLUS(plus(proper(z0), proper(z1)), proper(x1)), PROPER(plus(z0, z1)), PROPER(x1)) 389.10/118.86
PROPER(plus(x0, tt)) → c46(PLUS(proper(x0), ok(tt)), PROPER(x0)) 389.10/118.86
PROPER(plus(x0, 0)) → c46(PLUS(proper(x0), ok(0)), PROPER(x0)) 389.10/118.86
PROPER(plus(tt, x1)) → c46(PLUS(ok(tt), proper(x1)), PROPER(x1)) 389.10/118.86
PROPER(plus(0, x1)) → c46(PLUS(ok(0), proper(x1)), PROPER(x1)) 389.10/118.86
TOP(mark(U11(z0, z1))) → c49(TOP(U11(proper(z0), proper(z1))), PROPER(U11(z0, z1))) 389.10/118.86
TOP(mark(U12(z0))) → c49(TOP(U12(proper(z0))), PROPER(U12(z0))) 389.10/118.86
TOP(mark(isNat(z0))) → c49(TOP(isNat(proper(z0))), PROPER(isNat(z0))) 389.10/118.86
TOP(mark(U21(z0))) → c49(TOP(U21(proper(z0))), PROPER(U21(z0))) 389.10/118.86
TOP(mark(U31(z0, z1))) → c49(TOP(U31(proper(z0), proper(z1))), PROPER(U31(z0, z1))) 389.10/118.86
TOP(mark(U41(z0, z1, z2))) → c49(TOP(U41(proper(z0), proper(z1), proper(z2))), PROPER(U41(z0, z1, z2))) 389.10/118.86
TOP(mark(U42(z0, z1, z2))) → c49(TOP(U42(proper(z0), proper(z1), proper(z2))), PROPER(U42(z0, z1, z2))) 389.10/118.86
TOP(mark(s(z0))) → c49(TOP(s(proper(z0))), PROPER(s(z0))) 389.10/118.86
TOP(mark(plus(z0, z1))) → c49(TOP(plus(proper(z0), proper(z1))), PROPER(plus(z0, z1))) 389.10/118.86
TOP(ok(U11(tt, z0))) → c50(TOP(mark(U12(isNat(z0)))), ACTIVE(U11(tt, z0))) 389.10/118.86
TOP(ok(U12(tt))) → c50(TOP(mark(tt)), ACTIVE(U12(tt))) 389.10/118.86
TOP(ok(U21(tt))) → c50(TOP(mark(tt)), ACTIVE(U21(tt))) 389.10/118.86
TOP(ok(U31(tt, z0))) → c50(TOP(mark(z0)), ACTIVE(U31(tt, z0))) 389.10/118.86
TOP(ok(U41(tt, z0, z1))) → c50(TOP(mark(U42(isNat(z1), z0, z1))), ACTIVE(U41(tt, z0, z1))) 389.10/118.86
TOP(ok(U42(tt, z0, z1))) → c50(TOP(mark(s(plus(z1, z0)))), ACTIVE(U42(tt, z0, z1))) 389.10/118.86
TOP(ok(isNat(0))) → c50(TOP(mark(tt)), ACTIVE(isNat(0))) 389.10/118.86
TOP(ok(isNat(plus(z0, z1)))) → c50(TOP(mark(U11(isNat(z0), z1))), ACTIVE(isNat(plus(z0, z1)))) 389.10/118.86
TOP(ok(isNat(s(z0)))) → c50(TOP(mark(U21(isNat(z0)))), ACTIVE(isNat(s(z0)))) 389.10/118.86
TOP(ok(plus(z0, 0))) → c50(TOP(mark(U31(isNat(z0), z0))), ACTIVE(plus(z0, 0))) 389.10/118.86
TOP(ok(plus(z0, s(z1)))) → c50(TOP(mark(U41(isNat(z1), z1, z0))), ACTIVE(plus(z0, s(z1)))) 389.10/118.86
TOP(ok(U11(z0, z1))) → c50(TOP(U11(active(z0), z1)), ACTIVE(U11(z0, z1))) 389.10/118.86
TOP(ok(U12(z0))) → c50(TOP(U12(active(z0))), ACTIVE(U12(z0))) 389.10/118.86
TOP(ok(U21(z0))) → c50(TOP(U21(active(z0))), ACTIVE(U21(z0))) 389.10/118.86
TOP(ok(U31(z0, z1))) → c50(TOP(U31(active(z0), z1)), ACTIVE(U31(z0, z1))) 389.10/118.86
TOP(ok(U41(z0, z1, z2))) → c50(TOP(U41(active(z0), z1, z2)), ACTIVE(U41(z0, z1, z2))) 389.10/118.86
TOP(ok(U42(z0, z1, z2))) → c50(TOP(U42(active(z0), z1, z2)), ACTIVE(U42(z0, z1, z2))) 389.10/118.86
TOP(ok(s(z0))) → c50(TOP(s(active(z0))), ACTIVE(s(z0))) 389.10/118.86
TOP(ok(plus(z0, z1))) → c50(TOP(plus(active(z0), z1)), ACTIVE(plus(z0, z1))) 389.10/118.86
TOP(ok(plus(z0, z1))) → c50(TOP(plus(z0, active(z1))), ACTIVE(plus(z0, z1)))
389.10/118.86
389.10/118.86

(92) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.86
active(U12(tt)) → mark(tt) 389.10/118.86
active(U21(tt)) → mark(tt) 389.10/118.86
active(U31(tt, z0)) → mark(z0) 389.10/118.86
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.86
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.86
active(isNat(0)) → mark(tt) 389.10/118.86
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.86
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.86
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.86
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.86
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.86
active(U12(z0)) → U12(active(z0)) 389.10/118.86
active(U21(z0)) → U21(active(z0)) 389.10/118.86
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.86
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.86
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.86
active(s(z0)) → s(active(z0)) 389.10/118.86
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.86
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.86
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.86
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.86
U12(mark(z0)) → mark(U12(z0)) 389.10/118.86
U12(ok(z0)) → ok(U12(z0)) 389.10/118.86
U21(mark(z0)) → mark(U21(z0)) 389.10/118.86
U21(ok(z0)) → ok(U21(z0)) 389.10/118.86
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.86
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.86
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.86
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.86
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.86
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.86
s(mark(z0)) → mark(s(z0)) 389.10/118.86
s(ok(z0)) → ok(s(z0)) 389.10/118.86
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.86
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.86
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.86
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.86
proper(tt) → ok(tt) 389.10/118.86
proper(U12(z0)) → U12(proper(z0)) 389.10/118.86
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.86
proper(U21(z0)) → U21(proper(z0)) 389.10/118.86
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.86
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(s(z0)) → s(proper(z0)) 389.10/118.86
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.86
proper(0) → ok(0) 389.10/118.86
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.86
top(mark(z0)) → top(proper(z0)) 389.10/118.86
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.86
TOP(mark(tt)) → c49(TOP(ok(tt))) 389.10/118.86
TOP(mark(0)) → c49(TOP(ok(0)))
S tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.86
TOP(mark(tt)) → c49(TOP(ok(tt))) 389.10/118.86
TOP(mark(0)) → c49(TOP(ok(0)))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT, TOP

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48, c49

389.10/118.86
389.10/118.86

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

Removed 2 trailing tuple parts
389.10/118.86
389.10/118.86

(94) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.86
active(U12(tt)) → mark(tt) 389.10/118.86
active(U21(tt)) → mark(tt) 389.10/118.86
active(U31(tt, z0)) → mark(z0) 389.10/118.86
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.86
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.86
active(isNat(0)) → mark(tt) 389.10/118.86
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.86
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.86
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.86
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.86
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.86
active(U12(z0)) → U12(active(z0)) 389.10/118.86
active(U21(z0)) → U21(active(z0)) 389.10/118.86
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.86
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.86
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.86
active(s(z0)) → s(active(z0)) 389.10/118.86
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.86
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.86
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.86
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.86
U12(mark(z0)) → mark(U12(z0)) 389.10/118.86
U12(ok(z0)) → ok(U12(z0)) 389.10/118.86
U21(mark(z0)) → mark(U21(z0)) 389.10/118.86
U21(ok(z0)) → ok(U21(z0)) 389.10/118.86
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.86
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.86
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.86
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.86
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.86
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.86
s(mark(z0)) → mark(s(z0)) 389.10/118.86
s(ok(z0)) → ok(s(z0)) 389.10/118.86
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.86
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.86
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.86
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.86
proper(tt) → ok(tt) 389.10/118.86
proper(U12(z0)) → U12(proper(z0)) 389.10/118.86
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.86
proper(U21(z0)) → U21(proper(z0)) 389.10/118.86
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.86
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(s(z0)) → s(proper(z0)) 389.10/118.86
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.86
proper(0) → ok(0) 389.10/118.86
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.86
top(mark(z0)) → top(proper(z0)) 389.10/118.86
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.86
TOP(mark(tt)) → c49 389.10/118.86
TOP(mark(0)) → c49
S tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0)) 389.10/118.86
TOP(mark(tt)) → c49 389.10/118.86
TOP(mark(0)) → c49
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT, TOP

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48, c49

389.10/118.86
389.10/118.86

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

Removed 2 trailing nodes:

TOP(mark(0)) → c49 389.10/118.86
TOP(mark(tt)) → c49
389.10/118.86
389.10/118.86

(96) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.86
active(U12(tt)) → mark(tt) 389.10/118.86
active(U21(tt)) → mark(tt) 389.10/118.86
active(U31(tt, z0)) → mark(z0) 389.10/118.86
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.86
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.86
active(isNat(0)) → mark(tt) 389.10/118.86
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.86
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.86
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.86
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.86
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.86
active(U12(z0)) → U12(active(z0)) 389.10/118.86
active(U21(z0)) → U21(active(z0)) 389.10/118.86
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.86
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.86
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.86
active(s(z0)) → s(active(z0)) 389.10/118.86
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.86
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.86
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.86
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.86
U12(mark(z0)) → mark(U12(z0)) 389.10/118.86
U12(ok(z0)) → ok(U12(z0)) 389.10/118.86
U21(mark(z0)) → mark(U21(z0)) 389.10/118.86
U21(ok(z0)) → ok(U21(z0)) 389.10/118.86
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.86
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.86
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.86
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.86
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.86
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.86
s(mark(z0)) → mark(s(z0)) 389.10/118.86
s(ok(z0)) → ok(s(z0)) 389.10/118.86
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.86
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.86
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.86
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.86
proper(tt) → ok(tt) 389.10/118.86
proper(U12(z0)) → U12(proper(z0)) 389.10/118.86
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.86
proper(U21(z0)) → U21(proper(z0)) 389.10/118.86
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.86
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(s(z0)) → s(proper(z0)) 389.10/118.86
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.86
proper(0) → ok(0) 389.10/118.86
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.86
top(mark(z0)) → top(proper(z0)) 389.10/118.86
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
S tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
K tuples:none
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48

389.10/118.86
389.10/118.86

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

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

U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 389.10/118.86

POL(ISNAT(x1)) = 0    389.10/118.86
POL(PLUS(x1, x2)) = 0    389.10/118.86
POL(S(x1)) = 0    389.10/118.86
POL(U11'(x1, x2)) = 0    389.10/118.86
POL(U12'(x1)) = 0    389.10/118.86
POL(U21'(x1)) = 0    389.10/118.86
POL(U31'(x1, x2)) = [2]x1    389.10/118.86
POL(U41'(x1, x2, x3)) = 0    389.10/118.86
POL(U42'(x1, x2, x3)) = 0    389.10/118.86
POL(c20(x1)) = x1    389.10/118.86
POL(c21(x1)) = x1    389.10/118.86
POL(c22(x1)) = x1    389.10/118.86
POL(c23(x1)) = x1    389.10/118.86
POL(c24(x1)) = x1    389.10/118.86
POL(c25(x1)) = x1    389.10/118.86
POL(c26(x1)) = x1    389.10/118.86
POL(c27(x1)) = x1    389.10/118.86
POL(c28(x1)) = x1    389.10/118.86
POL(c29(x1)) = x1    389.10/118.86
POL(c30(x1)) = x1    389.10/118.86
POL(c31(x1)) = x1    389.10/118.86
POL(c32(x1)) = x1    389.10/118.86
POL(c33(x1)) = x1    389.10/118.86
POL(c34(x1)) = x1    389.10/118.86
POL(c35(x1)) = x1    389.10/118.86
POL(c36(x1)) = x1    389.10/118.86
POL(c48(x1)) = x1    389.10/118.86
POL(mark(x1)) = [4] + x1    389.10/118.86
POL(ok(x1)) = [1] + x1   
389.10/118.86
389.10/118.86

(98) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.86
active(U12(tt)) → mark(tt) 389.10/118.86
active(U21(tt)) → mark(tt) 389.10/118.86
active(U31(tt, z0)) → mark(z0) 389.10/118.86
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.86
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.86
active(isNat(0)) → mark(tt) 389.10/118.86
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.86
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.86
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.86
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.86
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.86
active(U12(z0)) → U12(active(z0)) 389.10/118.86
active(U21(z0)) → U21(active(z0)) 389.10/118.86
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.86
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.86
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.86
active(s(z0)) → s(active(z0)) 389.10/118.86
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.86
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.86
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.86
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.86
U12(mark(z0)) → mark(U12(z0)) 389.10/118.86
U12(ok(z0)) → ok(U12(z0)) 389.10/118.86
U21(mark(z0)) → mark(U21(z0)) 389.10/118.86
U21(ok(z0)) → ok(U21(z0)) 389.10/118.86
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.86
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.86
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.86
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.86
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.86
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.86
s(mark(z0)) → mark(s(z0)) 389.10/118.86
s(ok(z0)) → ok(s(z0)) 389.10/118.86
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.86
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.86
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.86
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.86
proper(tt) → ok(tt) 389.10/118.86
proper(U12(z0)) → U12(proper(z0)) 389.10/118.86
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.86
proper(U21(z0)) → U21(proper(z0)) 389.10/118.86
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.86
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(s(z0)) → s(proper(z0)) 389.10/118.86
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.86
proper(0) → ok(0) 389.10/118.86
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.86
top(mark(z0)) → top(proper(z0)) 389.10/118.86
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
S tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
K tuples:

U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1))
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48

389.10/118.86
389.10/118.86

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

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

U11'(mark(z0), z1) → c20(U11'(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 389.10/118.86

POL(ISNAT(x1)) = 0    389.10/118.86
POL(PLUS(x1, x2)) = 0    389.10/118.86
POL(S(x1)) = 0    389.10/118.86
POL(U11'(x1, x2)) = [2]x1    389.10/118.86
POL(U12'(x1)) = 0    389.10/118.86
POL(U21'(x1)) = 0    389.10/118.86
POL(U31'(x1, x2)) = [3]x1 + [5]x2    389.10/118.86
POL(U41'(x1, x2, x3)) = x2 + x3    389.10/118.86
POL(U42'(x1, x2, x3)) = x2    389.10/118.86
POL(c20(x1)) = x1    389.10/118.86
POL(c21(x1)) = x1    389.10/118.86
POL(c22(x1)) = x1    389.10/118.86
POL(c23(x1)) = x1    389.10/118.86
POL(c24(x1)) = x1    389.10/118.86
POL(c25(x1)) = x1    389.10/118.86
POL(c26(x1)) = x1    389.10/118.86
POL(c27(x1)) = x1    389.10/118.86
POL(c28(x1)) = x1    389.10/118.86
POL(c29(x1)) = x1    389.10/118.86
POL(c30(x1)) = x1    389.10/118.86
POL(c31(x1)) = x1    389.10/118.86
POL(c32(x1)) = x1    389.10/118.86
POL(c33(x1)) = x1    389.10/118.86
POL(c34(x1)) = x1    389.10/118.86
POL(c35(x1)) = x1    389.10/118.86
POL(c36(x1)) = x1    389.10/118.86
POL(c48(x1)) = x1    389.10/118.86
POL(mark(x1)) = [1] + x1    389.10/118.86
POL(ok(x1)) = x1   
389.10/118.86
389.10/118.86

(100) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.86
active(U12(tt)) → mark(tt) 389.10/118.86
active(U21(tt)) → mark(tt) 389.10/118.86
active(U31(tt, z0)) → mark(z0) 389.10/118.86
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.86
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.86
active(isNat(0)) → mark(tt) 389.10/118.86
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.86
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.86
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.86
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.86
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.86
active(U12(z0)) → U12(active(z0)) 389.10/118.86
active(U21(z0)) → U21(active(z0)) 389.10/118.86
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.86
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.86
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.86
active(s(z0)) → s(active(z0)) 389.10/118.86
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.86
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.86
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.86
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.86
U12(mark(z0)) → mark(U12(z0)) 389.10/118.86
U12(ok(z0)) → ok(U12(z0)) 389.10/118.86
U21(mark(z0)) → mark(U21(z0)) 389.10/118.86
U21(ok(z0)) → ok(U21(z0)) 389.10/118.86
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.86
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.86
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.86
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.86
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.86
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.86
s(mark(z0)) → mark(s(z0)) 389.10/118.86
s(ok(z0)) → ok(s(z0)) 389.10/118.86
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.86
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.86
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.86
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.86
proper(tt) → ok(tt) 389.10/118.86
proper(U12(z0)) → U12(proper(z0)) 389.10/118.86
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.86
proper(U21(z0)) → U21(proper(z0)) 389.10/118.86
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.86
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(s(z0)) → s(proper(z0)) 389.10/118.86
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.86
proper(0) → ok(0) 389.10/118.86
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.86
top(mark(z0)) → top(proper(z0)) 389.10/118.86
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
S tuples:

U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
K tuples:

U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U11'(mark(z0), z1) → c20(U11'(z0, z1))
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48

389.10/118.86
389.10/118.86

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

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

U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 389.10/118.86

POL(ISNAT(x1)) = 0    389.10/118.86
POL(PLUS(x1, x2)) = 0    389.10/118.86
POL(S(x1)) = 0    389.10/118.86
POL(U11'(x1, x2)) = x2    389.10/118.86
POL(U12'(x1)) = x1    389.10/118.86
POL(U21'(x1)) = 0    389.10/118.86
POL(U31'(x1, x2)) = [5]x1 + [3]x2    389.10/118.86
POL(U41'(x1, x2, x3)) = 0    389.10/118.86
POL(U42'(x1, x2, x3)) = 0    389.10/118.86
POL(c20(x1)) = x1    389.10/118.86
POL(c21(x1)) = x1    389.10/118.86
POL(c22(x1)) = x1    389.10/118.86
POL(c23(x1)) = x1    389.10/118.86
POL(c24(x1)) = x1    389.10/118.86
POL(c25(x1)) = x1    389.10/118.86
POL(c26(x1)) = x1    389.10/118.86
POL(c27(x1)) = x1    389.10/118.86
POL(c28(x1)) = x1    389.10/118.86
POL(c29(x1)) = x1    389.10/118.86
POL(c30(x1)) = x1    389.10/118.86
POL(c31(x1)) = x1    389.10/118.86
POL(c32(x1)) = x1    389.10/118.86
POL(c33(x1)) = x1    389.10/118.86
POL(c34(x1)) = x1    389.10/118.86
POL(c35(x1)) = x1    389.10/118.86
POL(c36(x1)) = x1    389.10/118.86
POL(c48(x1)) = x1    389.10/118.86
POL(mark(x1)) = [1] + x1    389.10/118.86
POL(ok(x1)) = [1] + x1   
389.10/118.86
389.10/118.86

(102) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.86
active(U12(tt)) → mark(tt) 389.10/118.86
active(U21(tt)) → mark(tt) 389.10/118.86
active(U31(tt, z0)) → mark(z0) 389.10/118.86
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.86
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.86
active(isNat(0)) → mark(tt) 389.10/118.86
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.86
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.86
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.86
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.86
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.86
active(U12(z0)) → U12(active(z0)) 389.10/118.86
active(U21(z0)) → U21(active(z0)) 389.10/118.86
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.86
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.86
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.86
active(s(z0)) → s(active(z0)) 389.10/118.86
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.86
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.86
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.86
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.86
U12(mark(z0)) → mark(U12(z0)) 389.10/118.86
U12(ok(z0)) → ok(U12(z0)) 389.10/118.86
U21(mark(z0)) → mark(U21(z0)) 389.10/118.86
U21(ok(z0)) → ok(U21(z0)) 389.10/118.86
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.86
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.86
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.86
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.86
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.86
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.86
s(mark(z0)) → mark(s(z0)) 389.10/118.86
s(ok(z0)) → ok(s(z0)) 389.10/118.86
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.86
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.86
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.86
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.86
proper(tt) → ok(tt) 389.10/118.86
proper(U12(z0)) → U12(proper(z0)) 389.10/118.86
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.86
proper(U21(z0)) → U21(proper(z0)) 389.10/118.86
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.86
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(s(z0)) → s(proper(z0)) 389.10/118.86
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.86
proper(0) → ok(0) 389.10/118.86
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.86
top(mark(z0)) → top(proper(z0)) 389.10/118.86
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
S tuples:

U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
K tuples:

U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0))
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48

389.10/118.86
389.10/118.86

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

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

PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 389.10/118.86

POL(ISNAT(x1)) = 0    389.10/118.86
POL(PLUS(x1, x2)) = [2]x1 + x2    389.10/118.86
POL(S(x1)) = 0    389.10/118.86
POL(U11'(x1, x2)) = [3]x1 + [5]x2    389.10/118.86
POL(U12'(x1)) = [3]x1    389.10/118.86
POL(U21'(x1)) = 0    389.10/118.86
POL(U31'(x1, x2)) = [3]x1 + [5]x2    389.10/118.86
POL(U41'(x1, x2, x3)) = 0    389.10/118.86
POL(U42'(x1, x2, x3)) = 0    389.10/118.86
POL(c20(x1)) = x1    389.10/118.86
POL(c21(x1)) = x1    389.10/118.86
POL(c22(x1)) = x1    389.10/118.86
POL(c23(x1)) = x1    389.10/118.86
POL(c24(x1)) = x1    389.10/118.86
POL(c25(x1)) = x1    389.10/118.86
POL(c26(x1)) = x1    389.10/118.86
POL(c27(x1)) = x1    389.10/118.86
POL(c28(x1)) = x1    389.10/118.86
POL(c29(x1)) = x1    389.10/118.86
POL(c30(x1)) = x1    389.10/118.86
POL(c31(x1)) = x1    389.10/118.86
POL(c32(x1)) = x1    389.10/118.86
POL(c33(x1)) = x1    389.10/118.86
POL(c34(x1)) = x1    389.10/118.86
POL(c35(x1)) = x1    389.10/118.86
POL(c36(x1)) = x1    389.10/118.86
POL(c48(x1)) = x1    389.10/118.86
POL(mark(x1)) = [1] + x1    389.10/118.86
POL(ok(x1)) = x1   
389.10/118.86
389.10/118.86

(104) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.86
active(U12(tt)) → mark(tt) 389.10/118.86
active(U21(tt)) → mark(tt) 389.10/118.86
active(U31(tt, z0)) → mark(z0) 389.10/118.86
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.86
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.86
active(isNat(0)) → mark(tt) 389.10/118.86
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.86
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.86
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.86
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.86
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.86
active(U12(z0)) → U12(active(z0)) 389.10/118.86
active(U21(z0)) → U21(active(z0)) 389.10/118.86
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.86
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.86
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.86
active(s(z0)) → s(active(z0)) 389.10/118.86
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.86
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.86
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.86
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.86
U12(mark(z0)) → mark(U12(z0)) 389.10/118.86
U12(ok(z0)) → ok(U12(z0)) 389.10/118.86
U21(mark(z0)) → mark(U21(z0)) 389.10/118.86
U21(ok(z0)) → ok(U21(z0)) 389.10/118.86
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.86
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.86
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.86
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.86
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.86
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.86
s(mark(z0)) → mark(s(z0)) 389.10/118.86
s(ok(z0)) → ok(s(z0)) 389.10/118.86
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.86
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.86
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.86
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.86
proper(tt) → ok(tt) 389.10/118.86
proper(U12(z0)) → U12(proper(z0)) 389.10/118.86
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.86
proper(U21(z0)) → U21(proper(z0)) 389.10/118.86
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.86
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(s(z0)) → s(proper(z0)) 389.10/118.86
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.86
proper(0) → ok(0) 389.10/118.86
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.86
top(mark(z0)) → top(proper(z0)) 389.10/118.86
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
S tuples:

U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
K tuples:

U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1))
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48

389.10/118.86
389.10/118.86

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

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

S(mark(z0)) → c32(S(z0))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 389.10/118.86

POL(ISNAT(x1)) = 0    389.10/118.86
POL(PLUS(x1, x2)) = 0    389.10/118.86
POL(S(x1)) = x1    389.10/118.86
POL(U11'(x1, x2)) = [3]x1 + [5]x2    389.10/118.86
POL(U12'(x1)) = [3]x1    389.10/118.86
POL(U21'(x1)) = 0    389.10/118.86
POL(U31'(x1, x2)) = [3]x1 + [5]x2    389.10/118.86
POL(U41'(x1, x2, x3)) = 0    389.10/118.86
POL(U42'(x1, x2, x3)) = 0    389.10/118.86
POL(c20(x1)) = x1    389.10/118.86
POL(c21(x1)) = x1    389.10/118.86
POL(c22(x1)) = x1    389.10/118.86
POL(c23(x1)) = x1    389.10/118.86
POL(c24(x1)) = x1    389.10/118.86
POL(c25(x1)) = x1    389.10/118.86
POL(c26(x1)) = x1    389.10/118.86
POL(c27(x1)) = x1    389.10/118.86
POL(c28(x1)) = x1    389.10/118.86
POL(c29(x1)) = x1    389.10/118.86
POL(c30(x1)) = x1    389.10/118.86
POL(c31(x1)) = x1    389.10/118.86
POL(c32(x1)) = x1    389.10/118.86
POL(c33(x1)) = x1    389.10/118.86
POL(c34(x1)) = x1    389.10/118.86
POL(c35(x1)) = x1    389.10/118.86
POL(c36(x1)) = x1    389.10/118.86
POL(c48(x1)) = x1    389.10/118.86
POL(mark(x1)) = [2] + x1    389.10/118.86
POL(ok(x1)) = x1   
389.10/118.86
389.10/118.86

(106) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.86
active(U12(tt)) → mark(tt) 389.10/118.86
active(U21(tt)) → mark(tt) 389.10/118.86
active(U31(tt, z0)) → mark(z0) 389.10/118.86
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.86
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.86
active(isNat(0)) → mark(tt) 389.10/118.86
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.86
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.86
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.86
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.86
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.86
active(U12(z0)) → U12(active(z0)) 389.10/118.86
active(U21(z0)) → U21(active(z0)) 389.10/118.86
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.86
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.86
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.86
active(s(z0)) → s(active(z0)) 389.10/118.86
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.86
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.86
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.86
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.86
U12(mark(z0)) → mark(U12(z0)) 389.10/118.86
U12(ok(z0)) → ok(U12(z0)) 389.10/118.86
U21(mark(z0)) → mark(U21(z0)) 389.10/118.86
U21(ok(z0)) → ok(U21(z0)) 389.10/118.86
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.86
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.86
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.86
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.86
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.86
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.86
s(mark(z0)) → mark(s(z0)) 389.10/118.86
s(ok(z0)) → ok(s(z0)) 389.10/118.86
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.86
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.86
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.86
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.86
proper(tt) → ok(tt) 389.10/118.86
proper(U12(z0)) → U12(proper(z0)) 389.10/118.86
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.86
proper(U21(z0)) → U21(proper(z0)) 389.10/118.86
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.86
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(s(z0)) → s(proper(z0)) 389.10/118.86
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.86
proper(0) → ok(0) 389.10/118.86
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.86
top(mark(z0)) → top(proper(z0)) 389.10/118.86
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
S tuples:

U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
K tuples:

U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
S(mark(z0)) → c32(S(z0))
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48

389.10/118.86
389.10/118.86

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

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

U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 389.10/118.86

POL(ISNAT(x1)) = 0    389.10/118.86
POL(PLUS(x1, x2)) = x1    389.10/118.86
POL(S(x1)) = x1    389.10/118.86
POL(U11'(x1, x2)) = [3]x1 + [5]x2    389.10/118.86
POL(U12'(x1)) = [3]x1    389.10/118.86
POL(U21'(x1)) = 0    389.10/118.86
POL(U31'(x1, x2)) = [5]x1 + [3]x2    389.10/118.86
POL(U41'(x1, x2, x3)) = 0    389.10/118.86
POL(U42'(x1, x2, x3)) = x1    389.10/118.86
POL(c20(x1)) = x1    389.10/118.86
POL(c21(x1)) = x1    389.10/118.86
POL(c22(x1)) = x1    389.10/118.86
POL(c23(x1)) = x1    389.10/118.86
POL(c24(x1)) = x1    389.10/118.86
POL(c25(x1)) = x1    389.10/118.86
POL(c26(x1)) = x1    389.10/118.86
POL(c27(x1)) = x1    389.10/118.86
POL(c28(x1)) = x1    389.10/118.86
POL(c29(x1)) = x1    389.10/118.86
POL(c30(x1)) = x1    389.10/118.86
POL(c31(x1)) = x1    389.10/118.86
POL(c32(x1)) = x1    389.10/118.86
POL(c33(x1)) = x1    389.10/118.86
POL(c34(x1)) = x1    389.10/118.86
POL(c35(x1)) = x1    389.10/118.86
POL(c36(x1)) = x1    389.10/118.86
POL(c48(x1)) = x1    389.10/118.86
POL(mark(x1)) = [1] + x1    389.10/118.86
POL(ok(x1)) = [2] + x1   
389.10/118.86
389.10/118.86

(108) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.86
active(U12(tt)) → mark(tt) 389.10/118.86
active(U21(tt)) → mark(tt) 389.10/118.86
active(U31(tt, z0)) → mark(z0) 389.10/118.86
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.86
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.86
active(isNat(0)) → mark(tt) 389.10/118.86
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.86
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.86
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.86
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.86
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.86
active(U12(z0)) → U12(active(z0)) 389.10/118.86
active(U21(z0)) → U21(active(z0)) 389.10/118.86
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.86
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.86
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.86
active(s(z0)) → s(active(z0)) 389.10/118.86
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.86
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.86
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.86
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.86
U12(mark(z0)) → mark(U12(z0)) 389.10/118.86
U12(ok(z0)) → ok(U12(z0)) 389.10/118.86
U21(mark(z0)) → mark(U21(z0)) 389.10/118.86
U21(ok(z0)) → ok(U21(z0)) 389.10/118.86
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.86
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.86
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.86
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.86
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.86
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.86
s(mark(z0)) → mark(s(z0)) 389.10/118.86
s(ok(z0)) → ok(s(z0)) 389.10/118.86
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.86
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.86
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.86
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.86
proper(tt) → ok(tt) 389.10/118.86
proper(U12(z0)) → U12(proper(z0)) 389.10/118.86
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.86
proper(U21(z0)) → U21(proper(z0)) 389.10/118.86
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.86
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(s(z0)) → s(proper(z0)) 389.10/118.86
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.86
proper(0) → ok(0) 389.10/118.86
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.86
top(mark(z0)) → top(proper(z0)) 389.10/118.86
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
S tuples:

U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
K tuples:

U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1))
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48

389.10/118.86
389.10/118.86

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

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

U21'(mark(z0)) → c24(U21'(z0))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 389.10/118.86

POL(ISNAT(x1)) = 0    389.10/118.86
POL(PLUS(x1, x2)) = [3]x1 + [3]x2    389.10/118.86
POL(S(x1)) = [3]x1    389.10/118.86
POL(U11'(x1, x2)) = [5]x1 + [5]x2    389.10/118.86
POL(U12'(x1)) = [3]x1    389.10/118.86
POL(U21'(x1)) = [2]x1    389.10/118.86
POL(U31'(x1, x2)) = [3]x1 + [5]x2    389.10/118.86
POL(U41'(x1, x2, x3)) = x2 + x3    389.10/118.86
POL(U42'(x1, x2, x3)) = [5]x1 + [5]x2 + [5]x3    389.10/118.86
POL(c20(x1)) = x1    389.10/118.86
POL(c21(x1)) = x1    389.10/118.86
POL(c22(x1)) = x1    389.10/118.86
POL(c23(x1)) = x1    389.10/118.86
POL(c24(x1)) = x1    389.10/118.86
POL(c25(x1)) = x1    389.10/118.86
POL(c26(x1)) = x1    389.10/118.86
POL(c27(x1)) = x1    389.10/118.86
POL(c28(x1)) = x1    389.10/118.86
POL(c29(x1)) = x1    389.10/118.86
POL(c30(x1)) = x1    389.10/118.86
POL(c31(x1)) = x1    389.10/118.86
POL(c32(x1)) = x1    389.10/118.86
POL(c33(x1)) = x1    389.10/118.86
POL(c34(x1)) = x1    389.10/118.86
POL(c35(x1)) = x1    389.10/118.86
POL(c36(x1)) = x1    389.10/118.86
POL(c48(x1)) = x1    389.10/118.86
POL(mark(x1)) = [1] + x1    389.10/118.86
POL(ok(x1)) = x1   
389.10/118.86
389.10/118.86

(110) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.86
active(U12(tt)) → mark(tt) 389.10/118.86
active(U21(tt)) → mark(tt) 389.10/118.86
active(U31(tt, z0)) → mark(z0) 389.10/118.86
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.86
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.86
active(isNat(0)) → mark(tt) 389.10/118.86
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.86
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.86
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.86
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.86
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.86
active(U12(z0)) → U12(active(z0)) 389.10/118.86
active(U21(z0)) → U21(active(z0)) 389.10/118.86
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.86
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.86
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.86
active(s(z0)) → s(active(z0)) 389.10/118.86
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.86
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.86
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.86
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.86
U12(mark(z0)) → mark(U12(z0)) 389.10/118.86
U12(ok(z0)) → ok(U12(z0)) 389.10/118.86
U21(mark(z0)) → mark(U21(z0)) 389.10/118.86
U21(ok(z0)) → ok(U21(z0)) 389.10/118.86
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.86
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.86
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.86
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.86
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.86
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.86
s(mark(z0)) → mark(s(z0)) 389.10/118.86
s(ok(z0)) → ok(s(z0)) 389.10/118.86
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.86
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.86
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.86
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.86
proper(tt) → ok(tt) 389.10/118.86
proper(U12(z0)) → U12(proper(z0)) 389.10/118.86
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.86
proper(U21(z0)) → U21(proper(z0)) 389.10/118.86
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.86
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.86
proper(s(z0)) → s(proper(z0)) 389.10/118.86
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.86
proper(0) → ok(0) 389.10/118.86
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.86
top(mark(z0)) → top(proper(z0)) 389.10/118.86
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
S tuples:

U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
K tuples:

U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0))
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48

389.10/118.86
389.10/118.86

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

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

U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.86
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.86
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.86
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.86
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.86
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.86
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.86
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.86
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.86
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.86
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.86
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.86
S(mark(z0)) → c32(S(z0)) 389.10/118.86
S(ok(z0)) → c33(S(z0)) 389.10/118.86
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.86
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.86
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.86
ISNAT(ok(z0)) → c48(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 389.10/118.86

POL(ISNAT(x1)) = 0    389.10/118.86
POL(PLUS(x1, x2)) = [5]x1 + [5]x2    389.10/118.86
POL(S(x1)) = [5]x1    389.10/118.86
POL(U11'(x1, x2)) = [5]x1 + [5]x2    389.10/118.86
POL(U12'(x1)) = [5]x1    389.10/118.86
POL(U21'(x1)) = 0    389.10/118.86
POL(U31'(x1, x2)) = [3]x1 + [5]x2    389.10/118.86
POL(U41'(x1, x2, x3)) = x3    389.10/118.86
POL(U42'(x1, x2, x3)) = [3]x1 + [5]x2 + [5]x3    389.10/118.86
POL(c20(x1)) = x1    389.10/118.86
POL(c21(x1)) = x1    389.10/118.86
POL(c22(x1)) = x1    389.10/118.86
POL(c23(x1)) = x1    389.10/118.86
POL(c24(x1)) = x1    389.10/118.86
POL(c25(x1)) = x1    389.10/118.86
POL(c26(x1)) = x1    389.10/118.86
POL(c27(x1)) = x1    389.10/118.86
POL(c28(x1)) = x1    389.10/118.86
POL(c29(x1)) = x1    389.10/118.86
POL(c30(x1)) = x1    389.10/118.86
POL(c31(x1)) = x1    389.10/118.86
POL(c32(x1)) = x1    389.10/118.86
POL(c33(x1)) = x1    389.10/118.86
POL(c34(x1)) = x1    389.10/118.86
POL(c35(x1)) = x1    389.10/118.86
POL(c36(x1)) = x1    389.10/118.86
POL(c48(x1)) = x1    389.10/118.86
POL(mark(x1)) = [5] + x1    389.10/118.86
POL(ok(x1)) = [1] + x1   
389.10/118.86
389.10/118.86

(112) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.86
active(U12(tt)) → mark(tt) 389.10/118.86
active(U21(tt)) → mark(tt) 389.10/118.86
active(U31(tt, z0)) → mark(z0) 389.10/118.86
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.86
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.86
active(isNat(0)) → mark(tt) 389.10/118.86
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.86
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.86
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.86
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.86
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.86
active(U12(z0)) → U12(active(z0)) 389.10/118.86
active(U21(z0)) → U21(active(z0)) 389.10/118.87
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.87
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.87
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.87
active(s(z0)) → s(active(z0)) 389.10/118.87
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.87
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.87
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.87
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.87
U12(mark(z0)) → mark(U12(z0)) 389.10/118.87
U12(ok(z0)) → ok(U12(z0)) 389.10/118.87
U21(mark(z0)) → mark(U21(z0)) 389.10/118.87
U21(ok(z0)) → ok(U21(z0)) 389.10/118.87
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.87
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.87
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.87
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.87
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.87
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.87
s(mark(z0)) → mark(s(z0)) 389.10/118.87
s(ok(z0)) → ok(s(z0)) 389.10/118.87
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.87
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.87
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.87
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.87
proper(tt) → ok(tt) 389.10/118.87
proper(U12(z0)) → U12(proper(z0)) 389.10/118.87
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.87
proper(U21(z0)) → U21(proper(z0)) 389.10/118.87
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.87
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.87
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.87
proper(s(z0)) → s(proper(z0)) 389.10/118.87
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.87
proper(0) → ok(0) 389.10/118.87
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.87
top(mark(z0)) → top(proper(z0)) 389.10/118.87
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.87
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.87
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.87
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.87
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.87
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.87
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.87
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.87
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.87
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.87
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.87
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.87
S(mark(z0)) → c32(S(z0)) 389.10/118.87
S(ok(z0)) → c33(S(z0)) 389.10/118.87
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.87
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.87
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.87
ISNAT(ok(z0)) → c48(ISNAT(z0))
S tuples:

U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.87
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.87
ISNAT(ok(z0)) → c48(ISNAT(z0))
K tuples:

U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.87
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.87
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.87
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.87
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.87
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.87
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.87
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.87
S(mark(z0)) → c32(S(z0)) 389.10/118.87
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.87
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.87
S(ok(z0)) → c33(S(z0)) 389.10/118.87
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.87
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.87
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2))
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48

389.10/118.87
389.10/118.87

(113) 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.

U21'(ok(z0)) → c25(U21'(z0))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.87
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.87
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.87
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.87
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.87
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.87
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.87
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.87
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.87
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.87
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.87
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.87
S(mark(z0)) → c32(S(z0)) 389.10/118.87
S(ok(z0)) → c33(S(z0)) 389.10/118.87
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.87
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.87
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.87
ISNAT(ok(z0)) → c48(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 389.10/118.87

POL(ISNAT(x1)) = 0    389.10/118.87
POL(PLUS(x1, x2)) = [3]x1 + [5]x2    389.10/118.87
POL(S(x1)) = [5]x1    389.10/118.87
POL(U11'(x1, x2)) = [3]x1 + [5]x2    389.10/118.87
POL(U12'(x1)) = [5]x1    389.10/118.87
POL(U21'(x1)) = [2]x1    389.10/118.87
POL(U31'(x1, x2)) = [5]x1 + [5]x2    389.10/118.87
POL(U41'(x1, x2, x3)) = [3]x2 + [5]x3    389.10/118.87
POL(U42'(x1, x2, x3)) = [5]x1 + [3]x2 + [5]x3    389.10/118.87
POL(c20(x1)) = x1    389.10/118.87
POL(c21(x1)) = x1    389.10/118.87
POL(c22(x1)) = x1    389.10/118.87
POL(c23(x1)) = x1    389.10/118.87
POL(c24(x1)) = x1    389.10/118.87
POL(c25(x1)) = x1    389.10/118.87
POL(c26(x1)) = x1    389.10/118.87
POL(c27(x1)) = x1    389.10/118.87
POL(c28(x1)) = x1    389.10/118.87
POL(c29(x1)) = x1    389.10/118.87
POL(c30(x1)) = x1    389.10/118.87
POL(c31(x1)) = x1    389.10/118.87
POL(c32(x1)) = x1    389.10/118.87
POL(c33(x1)) = x1    389.10/118.87
POL(c34(x1)) = x1    389.10/118.87
POL(c35(x1)) = x1    389.10/118.87
POL(c36(x1)) = x1    389.10/118.87
POL(c48(x1)) = x1    389.10/118.87
POL(mark(x1)) = [1] + x1    389.10/118.87
POL(ok(x1)) = [1] + x1   
389.10/118.87
389.10/118.87

(114) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.87
active(U12(tt)) → mark(tt) 389.10/118.87
active(U21(tt)) → mark(tt) 389.10/118.87
active(U31(tt, z0)) → mark(z0) 389.10/118.87
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.87
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.87
active(isNat(0)) → mark(tt) 389.10/118.87
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.87
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.87
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.87
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.87
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.87
active(U12(z0)) → U12(active(z0)) 389.10/118.87
active(U21(z0)) → U21(active(z0)) 389.10/118.87
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.87
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.87
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.87
active(s(z0)) → s(active(z0)) 389.10/118.87
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.87
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.87
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.87
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.87
U12(mark(z0)) → mark(U12(z0)) 389.10/118.87
U12(ok(z0)) → ok(U12(z0)) 389.10/118.87
U21(mark(z0)) → mark(U21(z0)) 389.10/118.87
U21(ok(z0)) → ok(U21(z0)) 389.10/118.87
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.87
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.87
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.87
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.87
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.87
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.87
s(mark(z0)) → mark(s(z0)) 389.10/118.87
s(ok(z0)) → ok(s(z0)) 389.10/118.87
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.87
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.87
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.87
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.87
proper(tt) → ok(tt) 389.10/118.87
proper(U12(z0)) → U12(proper(z0)) 389.10/118.87
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.87
proper(U21(z0)) → U21(proper(z0)) 389.10/118.87
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.87
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.87
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.87
proper(s(z0)) → s(proper(z0)) 389.10/118.87
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.87
proper(0) → ok(0) 389.10/118.87
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.87
top(mark(z0)) → top(proper(z0)) 389.10/118.87
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.87
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.87
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.87
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.87
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.87
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.87
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.87
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.87
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.87
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.87
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.87
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.87
S(mark(z0)) → c32(S(z0)) 389.10/118.87
S(ok(z0)) → c33(S(z0)) 389.10/118.87
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.87
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.87
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.87
ISNAT(ok(z0)) → c48(ISNAT(z0))
S tuples:

U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.87
ISNAT(ok(z0)) → c48(ISNAT(z0))
K tuples:

U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.87
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.87
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.87
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.87
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.87
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.87
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.87
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.87
S(mark(z0)) → c32(S(z0)) 389.10/118.87
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.87
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.87
S(ok(z0)) → c33(S(z0)) 389.10/118.87
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.87
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.87
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.87
U21'(ok(z0)) → c25(U21'(z0))
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48

389.10/118.87
389.10/118.87

(115) 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.

U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.87
ISNAT(ok(z0)) → c48(ISNAT(z0))
We considered the (Usable) Rules:none
And the Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.87
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.87
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.87
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.87
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.87
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.87
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.87
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.87
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.87
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.87
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.87
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.87
S(mark(z0)) → c32(S(z0)) 389.10/118.87
S(ok(z0)) → c33(S(z0)) 389.10/118.87
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.87
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.87
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.87
ISNAT(ok(z0)) → c48(ISNAT(z0))
The order we found is given by the following interpretation:
Polynomial interpretation : 389.10/118.87

POL(ISNAT(x1)) = x1    389.10/118.87
POL(PLUS(x1, x2)) = [5]x1 + [3]x2    389.10/118.87
POL(S(x1)) = [3]x1    389.10/118.87
POL(U11'(x1, x2)) = [5]x1 + [5]x2    389.10/118.87
POL(U12'(x1)) = [3]x1    389.10/118.87
POL(U21'(x1)) = [3]x1    389.10/118.87
POL(U31'(x1, x2)) = [3]x1 + [5]x2    389.10/118.87
POL(U41'(x1, x2, x3)) = [2]x1 + [5]x2 + [5]x3    389.10/118.87
POL(U42'(x1, x2, x3)) = [3]x1 + [3]x2 + [5]x3    389.10/118.87
POL(c20(x1)) = x1    389.10/118.87
POL(c21(x1)) = x1    389.10/118.87
POL(c22(x1)) = x1    389.10/118.87
POL(c23(x1)) = x1    389.10/118.87
POL(c24(x1)) = x1    389.10/118.87
POL(c25(x1)) = x1    389.10/118.87
POL(c26(x1)) = x1    389.10/118.87
POL(c27(x1)) = x1    389.10/118.87
POL(c28(x1)) = x1    389.10/118.87
POL(c29(x1)) = x1    389.10/118.87
POL(c30(x1)) = x1    389.10/118.87
POL(c31(x1)) = x1    389.10/118.87
POL(c32(x1)) = x1    389.10/118.87
POL(c33(x1)) = x1    389.10/118.87
POL(c34(x1)) = x1    389.10/118.87
POL(c35(x1)) = x1    389.10/118.87
POL(c36(x1)) = x1    389.10/118.87
POL(c48(x1)) = x1    389.10/118.87
POL(mark(x1)) = [1] + x1    389.10/118.87
POL(ok(x1)) = [1] + x1   
389.10/118.87
389.10/118.87

(116) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U11(tt, z0)) → mark(U12(isNat(z0))) 389.10/118.87
active(U12(tt)) → mark(tt) 389.10/118.87
active(U21(tt)) → mark(tt) 389.10/118.87
active(U31(tt, z0)) → mark(z0) 389.10/118.87
active(U41(tt, z0, z1)) → mark(U42(isNat(z1), z0, z1)) 389.10/118.87
active(U42(tt, z0, z1)) → mark(s(plus(z1, z0))) 389.10/118.87
active(isNat(0)) → mark(tt) 389.10/118.87
active(isNat(plus(z0, z1))) → mark(U11(isNat(z0), z1)) 389.10/118.87
active(isNat(s(z0))) → mark(U21(isNat(z0))) 389.10/118.87
active(plus(z0, 0)) → mark(U31(isNat(z0), z0)) 389.10/118.87
active(plus(z0, s(z1))) → mark(U41(isNat(z1), z1, z0)) 389.10/118.87
active(U11(z0, z1)) → U11(active(z0), z1) 389.10/118.87
active(U12(z0)) → U12(active(z0)) 389.10/118.87
active(U21(z0)) → U21(active(z0)) 389.10/118.87
active(U31(z0, z1)) → U31(active(z0), z1) 389.10/118.87
active(U41(z0, z1, z2)) → U41(active(z0), z1, z2) 389.10/118.87
active(U42(z0, z1, z2)) → U42(active(z0), z1, z2) 389.10/118.87
active(s(z0)) → s(active(z0)) 389.10/118.87
active(plus(z0, z1)) → plus(active(z0), z1) 389.10/118.87
active(plus(z0, z1)) → plus(z0, active(z1)) 389.10/118.87
U11(mark(z0), z1) → mark(U11(z0, z1)) 389.10/118.87
U11(ok(z0), ok(z1)) → ok(U11(z0, z1)) 389.10/118.87
U12(mark(z0)) → mark(U12(z0)) 389.10/118.87
U12(ok(z0)) → ok(U12(z0)) 389.10/118.87
U21(mark(z0)) → mark(U21(z0)) 389.10/118.87
U21(ok(z0)) → ok(U21(z0)) 389.10/118.87
U31(mark(z0), z1) → mark(U31(z0, z1)) 389.10/118.87
U31(ok(z0), ok(z1)) → ok(U31(z0, z1)) 389.10/118.87
U41(mark(z0), z1, z2) → mark(U41(z0, z1, z2)) 389.10/118.87
U41(ok(z0), ok(z1), ok(z2)) → ok(U41(z0, z1, z2)) 389.10/118.87
U42(mark(z0), z1, z2) → mark(U42(z0, z1, z2)) 389.10/118.87
U42(ok(z0), ok(z1), ok(z2)) → ok(U42(z0, z1, z2)) 389.10/118.87
s(mark(z0)) → mark(s(z0)) 389.10/118.87
s(ok(z0)) → ok(s(z0)) 389.10/118.87
plus(mark(z0), z1) → mark(plus(z0, z1)) 389.10/118.87
plus(z0, mark(z1)) → mark(plus(z0, z1)) 389.10/118.87
plus(ok(z0), ok(z1)) → ok(plus(z0, z1)) 389.10/118.87
proper(U11(z0, z1)) → U11(proper(z0), proper(z1)) 389.10/118.87
proper(tt) → ok(tt) 389.10/118.87
proper(U12(z0)) → U12(proper(z0)) 389.10/118.87
proper(isNat(z0)) → isNat(proper(z0)) 389.10/118.87
proper(U21(z0)) → U21(proper(z0)) 389.10/118.87
proper(U31(z0, z1)) → U31(proper(z0), proper(z1)) 389.10/118.87
proper(U41(z0, z1, z2)) → U41(proper(z0), proper(z1), proper(z2)) 389.10/118.87
proper(U42(z0, z1, z2)) → U42(proper(z0), proper(z1), proper(z2)) 389.10/118.87
proper(s(z0)) → s(proper(z0)) 389.10/118.87
proper(plus(z0, z1)) → plus(proper(z0), proper(z1)) 389.10/118.87
proper(0) → ok(0) 389.10/118.87
isNat(ok(z0)) → ok(isNat(z0)) 389.10/118.87
top(mark(z0)) → top(proper(z0)) 389.10/118.87
top(ok(z0)) → top(active(z0))
Tuples:

U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.87
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.87
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.87
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.87
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.87
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.87
U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.87
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.87
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.87
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.87
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.87
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.87
S(mark(z0)) → c32(S(z0)) 389.10/118.87
S(ok(z0)) → c33(S(z0)) 389.10/118.87
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.87
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.87
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.87
ISNAT(ok(z0)) → c48(ISNAT(z0))
S tuples:none
K tuples:

U31'(mark(z0), z1) → c26(U31'(z0, z1)) 389.10/118.87
U31'(ok(z0), ok(z1)) → c27(U31'(z0, z1)) 389.10/118.87
U11'(mark(z0), z1) → c20(U11'(z0, z1)) 389.10/118.87
U11'(ok(z0), ok(z1)) → c21(U11'(z0, z1)) 389.10/118.87
U12'(mark(z0)) → c22(U12'(z0)) 389.10/118.87
U12'(ok(z0)) → c23(U12'(z0)) 389.10/118.87
PLUS(mark(z0), z1) → c34(PLUS(z0, z1)) 389.10/118.87
PLUS(z0, mark(z1)) → c35(PLUS(z0, z1)) 389.10/118.87
S(mark(z0)) → c32(S(z0)) 389.10/118.87
U42'(mark(z0), z1, z2) → c30(U42'(z0, z1, z2)) 389.10/118.87
U42'(ok(z0), ok(z1), ok(z2)) → c31(U42'(z0, z1, z2)) 389.10/118.87
S(ok(z0)) → c33(S(z0)) 389.10/118.87
PLUS(ok(z0), ok(z1)) → c36(PLUS(z0, z1)) 389.10/118.87
U21'(mark(z0)) → c24(U21'(z0)) 389.10/118.87
U41'(ok(z0), ok(z1), ok(z2)) → c29(U41'(z0, z1, z2)) 389.10/118.87
U21'(ok(z0)) → c25(U21'(z0)) 389.10/118.87
U41'(mark(z0), z1, z2) → c28(U41'(z0, z1, z2)) 389.10/118.87
ISNAT(ok(z0)) → c48(ISNAT(z0))
Defined Rule Symbols:

active, U11, U12, U21, U31, U41, U42, s, plus, proper, isNat, top

Defined Pair Symbols:

U11', U12', U21', U31', U41', U42', S, PLUS, ISNAT

Compound Symbols:

c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c48

389.10/118.87
389.10/118.87

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

The set S is empty
389.10/118.87
389.10/118.87

(118) BOUNDS(O(1), O(1))

389.10/118.87
389.10/118.87
389.43/119.00 EOF