Runtime Complexity of the query pattern
div(g,g,a)
w.r.t. the given Prolog program could be shown to be BOUNDS(O(1), O(n^1)).

0 Prolog
↳1 LPReorderTransformerProof (⇔, 0 ms)
↳2 Prolog
↳3 PrologToCdtProblemTransformerProof (UPPER BOUND (ID), 1662 ms)
↳4 CdtProblem
    ↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳6 CdtProblem
    ↳7 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 6 ms)
    ↳8 CdtProblem
    ↳9 CdtKnowledgeProof (⇔, 25 ms)
    ↳10 CdtProblem
    ↳11 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 344 ms)
    ↳12 CdtProblem
    ↳13 CdtGraphRemoveDanglingProof (ComplexityIfPolyImplication, 0 ms)
    ↳14 CdtProblem
    ↳15 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳16 CdtProblem
    ↳17 CdtInstantiationProof (BOTH BOUNDS(ID, ID), 40 ms)
    ↳18 CdtProblem
    ↳19 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 169 ms)
    ↳20 CdtProblem
    ↳21 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 2 ms)
    ↳22 CdtProblem
    ↳23 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳24 CdtProblem
    ↳25 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳26 CdtProblem
    ↳27 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳28 CdtProblem
    ↳29 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳30 CdtProblem
    ↳31 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳32 CdtProblem
    ↳33 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳34 CdtProblem
↳35 PrologToCdtProblemTransformerProof (UPPER BOUND (ID), 1556 ms)
↳36 CdtProblem
    ↳37 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 16 ms)
    ↳38 CdtProblem
    ↳39 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳40 CdtProblem
    ↳41 CdtKnowledgeProof (⇔, 1 ms)
    ↳42 CdtProblem
    ↳43 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 308 ms)
    ↳44 CdtProblem
    ↳45 CdtGraphRemoveDanglingProof (ComplexityIfPolyImplication, 0 ms)
    ↳46 CdtProblem
    ↳47 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳48 CdtProblem
    ↳49 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 57 ms)
    ↳50 CdtProblem
    ↳51 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 209 ms)
    ↳52 CdtProblem
    ↳53 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳54 CdtProblem
    ↳55 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳56 CdtProblem
    ↳57 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳58 CdtProblem
    ↳59 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳60 CdtProblem
    ↳61 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳62 CdtProblem
    ↳63 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳64 CdtProblem
    ↳65 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳66 CdtProblem
    ↳67 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳68 CdtProblem
    ↳69 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳70 CdtProblem
    ↳71 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳72 CdtProblem
    ↳73 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 19 ms)
    ↳74 CdtProblem
    ↳75 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳76 CdtProblem
    ↳77 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳78 CdtProblem
    ↳79 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳80 CdtProblem
    ↳81 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳82 CdtProblem
    ↳83 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳84 CdtProblem
    ↳85 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳86 CdtProblem
    ↳87 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 2 ms)
    ↳88 CdtProblem
    ↳89 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳90 CdtProblem
    ↳91 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳92 CdtProblem
    ↳93 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳94 CdtProblem
    ↳95 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳96 CdtProblem
    ↳97 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳98 CdtProblem
    ↳99 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳100 CdtProblem
    ↳101 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳102 CdtProblem
    ↳103 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 11 ms)
    ↳104 CdtProblem
    ↳105 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳106 CdtProblem
    ↳107 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳108 CdtProblem
    ↳109 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳110 CdtProblem
    ↳111 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳112 CdtProblem
    ↳113 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳114 CdtProblem
    ↳115 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 3 ms)
    ↳116 CdtProblem
    ↳117 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳118 CdtProblem
    ↳119 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳120 CdtProblem
    ↳121 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳122 CdtProblem
    ↳123 CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID), 0 ms)
    ↳124 CdtProblem
    ↳125 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 2 ms)
    ↳126 CdtProblem
    ↳127 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 594 ms)
    ↳128 CdtProblem
    ↳129 CdtKnowledgeProof (⇔, 0 ms)
    ↳130 CdtProblem
    ↳131 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 676 ms)
    ↳132 CdtProblem
    ↳133 CdtKnowledgeProof (⇔, 0 ms)
    ↳134 CdtProblem
    ↳135 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 255 ms)
    ↳136 CdtProblem
    ↳137 CdtKnowledgeProof (⇔, 0 ms)
    ↳138 CdtProblem
    ↳139 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 277 ms)
    ↳140 CdtProblem
    ↳141 CdtKnowledgeProof (⇔, 0 ms)
    ↳142 CdtProblem
    ↳143 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 195 ms)
    ↳144 CdtProblem
    ↳145 CdtKnowledgeProof (⇔, 0 ms)
    ↳146 CdtProblem
    ↳147 CdtPolyRedPairProof (UPPER BOUND (ADD(O(n^1))), 191 ms)
    ↳148 CdtProblem
    ↳149 CdtKnowledgeProof (⇔, 0 ms)
    ↳150 BOUNDS(O(1), O(1))

(0) Obligation:

Clauses:

div(X, Y, Z) :- quot(X, Y, Y, Z).
quot(0, s(Y), s(Z), 0).
quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U).
quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U).

Query: div(g,g,a)

(1) LPReorderTransformerProof (EQUIVALENT transformation)

Reordered facts before rules in definite LP [PROLOG].

(2) Obligation:

Clauses:

quot(0, s(Y), s(Z), 0).
div(X, Y, Z) :- quot(X, Y, Y, Z).
quot(s(X), s(Y), Z, U) :- quot(X, Y, Z, U).
quot(X, 0, s(Z), s(U)) :- quot(X, s(Z), s(Z), U).

Query: div(g,g,a)

(3) PrologToCdtProblemTransformerProof (UPPER BOUND (ID) transformation)

Built complexity over-approximating cdt problems from derivation graph.

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F1_IN(z0, z1) → c(U1'(f7_in(z0, z1), z0, z1), F7_IN(z0, z1))
F860_IN(z0) → c3(U2'(f866_in(z0), z0), F866_IN(z0))
F816_IN(z0) → c7(U3'(f824_in(z0), z0), F824_IN(z0))
F167_IN(z0, z1, z2) → c11(U4'(f174_in(z0, z1, z2), z0, z1, z2), F174_IN(z0, z1, z2))
F736_IN(z0) → c15(U5'(f745_in(z0), z0), F745_IN(z0))
F7_IN(z0, z1) → c19(U6'(f15_in(z0, z1), z0, z1), F15_IN(z0, z1))
F633_IN(z0) → c23(U7'(f642_in(z0), z0), F642_IN(z0))
F507_IN(z0) → c27(U8'(f514_in(z0), z0), F514_IN(z0))
F363_IN(z0) → c31(U9'(f371_in(z0), z0), F371_IN(z0))
F194_IN(z0) → c35(U10'(f202_in(z0), z0), F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(U11'(f35_in(z0, z1), s(z0), s(z1)), F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(U12'(f50_in(z0, z1), s(z0), s(z1)), F50_IN(z0, z1))
F42_IN(z0, 0) → c46(U13'(f860_in(z0), z0, 0), F860_IN(z0))
F59_IN(s(z0), s(z1)) → c49(U14'(f70_in(z0, z1), s(z0), s(z1)), F70_IN(z0, z1))
F60_IN(z0, 0) → c52(U15'(f816_in(z0), z0, 0), F816_IN(z0))
F870_IN(s(z0)) → c54(U16'(f860_in(z0), s(z0)), F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(U17'(f91_in(z0, z1), s(z0), s(z1)), F91_IN(z0, z1))
F80_IN(z0, 0) → c60(U18'(f736_in(z0), z0, 0), F736_IN(z0))
F829_IN(s(z0)) → c63(U19'(f837_in(z0), s(z0)), F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(U20'(f110_in(z0, z1), s(z0), s(z1)), F110_IN(z0, z1))
F100_IN(z0, 0) → c70(U21'(f633_in(z0), z0, 0), F633_IN(z0))
F751_IN(s(z0)) → c73(U22'(f765_in(z0), s(z0)), F765_IN(z0))
F841_IN(s(z0)) → c76(U23'(f816_in(z0), s(z0)), F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(U24'(f131_in(z0, z1), s(z0), s(z1)), F131_IN(z0, z1))
F120_IN(z0, 0) → c82(U25'(f507_in(z0), z0, 0), F507_IN(z0))
F649_IN(s(z0)) → c85(U26'(f662_in(z0), s(z0)), F662_IN(z0))
F771_IN(s(z0)) → c89(U27'(f787_in(z0), s(z0)), F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(U28'(f151_in(z0, z1), s(z0), s(z1)), F151_IN(z0, z1))
F140_IN(z0, 0) → c96(U29'(f363_in(z0), z0, 0), F363_IN(z0))
F523_IN(s(z0)) → c99(U30'(f534_in(z0), s(z0)), F534_IN(z0))
F669_IN(s(z0)) → c103(U31'(f682_in(z0), s(z0)), F682_IN(z0))
F793_IN(s(z0)) → c106(U32'(f736_in(z0), s(z0)), F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(U33'(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1)), F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F161_IN(z0, 0) → c110(U34'(f194_in(z0), z0, 0), F194_IN(z0))
F379_IN(s(z0)) → c113(U35'(f391_in(z0), s(z0)), F391_IN(z0))
F543_IN(s(z0)) → c117(U36'(f554_in(z0), s(z0)), F554_IN(z0))
F689_IN(s(z0)) → c121(U37'(f703_in(z0), s(z0)), F703_IN(z0))
F210_IN(s(z0)) → c125(U38'(f223_in(z0), s(z0)), F223_IN(z0))
F399_IN(s(z0)) → c129(U39'(f411_in(z0), s(z0)), F411_IN(z0))
F563_IN(s(z0)) → c133(U40'(f574_in(z0), s(z0)), F574_IN(z0))
F709_IN(s(z0)) → c136(U41'(f633_in(z0), s(z0)), F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(U42'(f167_in(z0, z1, z2), s(z0), s(z1), z2), F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(U43'(f7_in(z0, s(z1)), z0, 0, z1), F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(U44'(f243_in(z0), s(z0)), F243_IN(z0))
F419_IN(s(z0)) → c147(U45'(f433_in(z0), s(z0)), F433_IN(z0))
F583_IN(s(z0)) → c151(U46'(f598_in(z0), s(z0)), F598_IN(z0))
F250_IN(s(z0)) → c155(U47'(f263_in(z0), s(z0)), F263_IN(z0))
F439_IN(s(z0)) → c159(U48'(f448_in(z0), s(z0)), F448_IN(z0))
F605_IN(s(z0)) → c162(U49'(f507_in(z0), s(z0)), F507_IN(z0))
F271_IN(s(z0)) → c165(U50'(f283_in(z0), s(z0)), F283_IN(z0))
F457_IN(s(z0)) → c169(U51'(f468_in(z0), s(z0)), F468_IN(z0))
F291_IN(s(z0)) → c173(U52'(f303_in(z0), s(z0)), F303_IN(z0))
F477_IN(s(z0)) → c176(U53'(f363_in(z0), s(z0)), F363_IN(z0))
F311_IN(s(z0)) → c179(U54'(f323_in(z0), s(z0)), F323_IN(z0))
F331_IN(s(z0)) → c182(U55'(f194_in(z0), s(z0)), F194_IN(z0))
F15_IN(z0, z1) → c184(U56'(f21_in(z0, z1), f22_in(z0, z1), z0, z1), F21_IN(z0, z1))
F35_IN(z0, z1) → c187(U57'(f41_in(z0, z1), f42_in(z0, z1), z0, z1), F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(U58'(f59_in(z0, z1), f60_in(z0, z1), z0, z1), F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(U59'(f79_in(z0, z1), f80_in(z0, z1), z0, z1), F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(U60'(f99_in(z0, z1), f100_in(z0, z1), z0, z1), F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(U61'(f119_in(z0, z1), f120_in(z0, z1), z0, z1), F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(U62'(f139_in(z0, z1), f140_in(z0, z1), z0, z1), F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(U63'(f159_in(z0, z1), f161_in(z0, z1), z0, z1), F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(U64'(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2), F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(U65'(f210_in(z0), f212_in(z0), z0), F210_IN(z0))
F223_IN(z0) → c214(U66'(f230_in(z0), f232_in(z0), z0), F230_IN(z0))
F243_IN(z0) → c217(U67'(f250_in(z0), f252_in(z0), z0), F250_IN(z0))
F263_IN(z0) → c220(U68'(f271_in(z0), f272_in(z0), z0), F271_IN(z0))
F283_IN(z0) → c223(U69'(f291_in(z0), f292_in(z0), z0), F291_IN(z0))
F303_IN(z0) → c226(U70'(f311_in(z0), f312_in(z0), z0), F311_IN(z0))
F323_IN(z0) → c229(U71'(f331_in(z0), f332_in(z0), z0), F331_IN(z0))
F371_IN(z0) → c232(U72'(f379_in(z0), f380_in(z0), z0), F379_IN(z0))
F391_IN(z0) → c235(U73'(f399_in(z0), f400_in(z0), z0), F399_IN(z0))
F411_IN(z0) → c238(U74'(f419_in(z0), f420_in(z0), z0), F419_IN(z0))
F433_IN(z0) → c241(U75'(f439_in(z0), f440_in(z0), z0), F439_IN(z0))
F448_IN(z0) → c244(U76'(f457_in(z0), f458_in(z0), z0), F457_IN(z0))
F468_IN(z0) → c247(U77'(f477_in(z0), f478_in(z0), z0), F477_IN(z0))
F514_IN(z0) → c250(U78'(f523_in(z0), f524_in(z0), z0), F523_IN(z0))
F534_IN(z0) → c253(U79'(f543_in(z0), f544_in(z0), z0), F543_IN(z0))
F554_IN(z0) → c256(U80'(f563_in(z0), f564_in(z0), z0), F563_IN(z0))
F574_IN(z0) → c259(U81'(f583_in(z0), f584_in(z0), z0), F583_IN(z0))
F598_IN(z0) → c262(U82'(f605_in(z0), f606_in(z0), z0), F605_IN(z0))
F642_IN(z0) → c265(U83'(f649_in(z0), f650_in(z0), z0), F649_IN(z0))
F662_IN(z0) → c268(U84'(f669_in(z0), f670_in(z0), z0), F669_IN(z0))
F682_IN(z0) → c271(U85'(f689_in(z0), f690_in(z0), z0), F689_IN(z0))
F703_IN(z0) → c274(U86'(f709_in(z0), f710_in(z0), z0), F709_IN(z0))
F745_IN(z0) → c277(U87'(f751_in(z0), f752_in(z0), z0), F751_IN(z0))
F765_IN(z0) → c280(U88'(f771_in(z0), f772_in(z0), z0), F771_IN(z0))
F787_IN(z0) → c283(U89'(f793_in(z0), f794_in(z0), z0), F793_IN(z0))
F824_IN(z0) → c286(U90'(f829_in(z0), f830_in(z0), z0), F829_IN(z0))
F837_IN(z0) → c289(U91'(f841_in(z0), f842_in(z0), z0), F841_IN(z0))
F866_IN(z0) → c292(U92'(f870_in(z0), f871_in(z0), z0), F870_IN(z0))
S tuples:

F1_IN(z0, z1) → c(U1'(f7_in(z0, z1), z0, z1), F7_IN(z0, z1))
F860_IN(z0) → c3(U2'(f866_in(z0), z0), F866_IN(z0))
F816_IN(z0) → c7(U3'(f824_in(z0), z0), F824_IN(z0))
F167_IN(z0, z1, z2) → c11(U4'(f174_in(z0, z1, z2), z0, z1, z2), F174_IN(z0, z1, z2))
F736_IN(z0) → c15(U5'(f745_in(z0), z0), F745_IN(z0))
F7_IN(z0, z1) → c19(U6'(f15_in(z0, z1), z0, z1), F15_IN(z0, z1))
F633_IN(z0) → c23(U7'(f642_in(z0), z0), F642_IN(z0))
F507_IN(z0) → c27(U8'(f514_in(z0), z0), F514_IN(z0))
F363_IN(z0) → c31(U9'(f371_in(z0), z0), F371_IN(z0))
F194_IN(z0) → c35(U10'(f202_in(z0), z0), F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(U11'(f35_in(z0, z1), s(z0), s(z1)), F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(U12'(f50_in(z0, z1), s(z0), s(z1)), F50_IN(z0, z1))
F42_IN(z0, 0) → c46(U13'(f860_in(z0), z0, 0), F860_IN(z0))
F59_IN(s(z0), s(z1)) → c49(U14'(f70_in(z0, z1), s(z0), s(z1)), F70_IN(z0, z1))
F60_IN(z0, 0) → c52(U15'(f816_in(z0), z0, 0), F816_IN(z0))
F870_IN(s(z0)) → c54(U16'(f860_in(z0), s(z0)), F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(U17'(f91_in(z0, z1), s(z0), s(z1)), F91_IN(z0, z1))
F80_IN(z0, 0) → c60(U18'(f736_in(z0), z0, 0), F736_IN(z0))
F829_IN(s(z0)) → c63(U19'(f837_in(z0), s(z0)), F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(U20'(f110_in(z0, z1), s(z0), s(z1)), F110_IN(z0, z1))
F100_IN(z0, 0) → c70(U21'(f633_in(z0), z0, 0), F633_IN(z0))
F751_IN(s(z0)) → c73(U22'(f765_in(z0), s(z0)), F765_IN(z0))
F841_IN(s(z0)) → c76(U23'(f816_in(z0), s(z0)), F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(U24'(f131_in(z0, z1), s(z0), s(z1)), F131_IN(z0, z1))
F120_IN(z0, 0) → c82(U25'(f507_in(z0), z0, 0), F507_IN(z0))
F649_IN(s(z0)) → c85(U26'(f662_in(z0), s(z0)), F662_IN(z0))
F771_IN(s(z0)) → c89(U27'(f787_in(z0), s(z0)), F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(U28'(f151_in(z0, z1), s(z0), s(z1)), F151_IN(z0, z1))
F140_IN(z0, 0) → c96(U29'(f363_in(z0), z0, 0), F363_IN(z0))
F523_IN(s(z0)) → c99(U30'(f534_in(z0), s(z0)), F534_IN(z0))
F669_IN(s(z0)) → c103(U31'(f682_in(z0), s(z0)), F682_IN(z0))
F793_IN(s(z0)) → c106(U32'(f736_in(z0), s(z0)), F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(U33'(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1)), F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F161_IN(z0, 0) → c110(U34'(f194_in(z0), z0, 0), F194_IN(z0))
F379_IN(s(z0)) → c113(U35'(f391_in(z0), s(z0)), F391_IN(z0))
F543_IN(s(z0)) → c117(U36'(f554_in(z0), s(z0)), F554_IN(z0))
F689_IN(s(z0)) → c121(U37'(f703_in(z0), s(z0)), F703_IN(z0))
F210_IN(s(z0)) → c125(U38'(f223_in(z0), s(z0)), F223_IN(z0))
F399_IN(s(z0)) → c129(U39'(f411_in(z0), s(z0)), F411_IN(z0))
F563_IN(s(z0)) → c133(U40'(f574_in(z0), s(z0)), F574_IN(z0))
F709_IN(s(z0)) → c136(U41'(f633_in(z0), s(z0)), F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(U42'(f167_in(z0, z1, z2), s(z0), s(z1), z2), F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(U43'(f7_in(z0, s(z1)), z0, 0, z1), F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(U44'(f243_in(z0), s(z0)), F243_IN(z0))
F419_IN(s(z0)) → c147(U45'(f433_in(z0), s(z0)), F433_IN(z0))
F583_IN(s(z0)) → c151(U46'(f598_in(z0), s(z0)), F598_IN(z0))
F250_IN(s(z0)) → c155(U47'(f263_in(z0), s(z0)), F263_IN(z0))
F439_IN(s(z0)) → c159(U48'(f448_in(z0), s(z0)), F448_IN(z0))
F605_IN(s(z0)) → c162(U49'(f507_in(z0), s(z0)), F507_IN(z0))
F271_IN(s(z0)) → c165(U50'(f283_in(z0), s(z0)), F283_IN(z0))
F457_IN(s(z0)) → c169(U51'(f468_in(z0), s(z0)), F468_IN(z0))
F291_IN(s(z0)) → c173(U52'(f303_in(z0), s(z0)), F303_IN(z0))
F477_IN(s(z0)) → c176(U53'(f363_in(z0), s(z0)), F363_IN(z0))
F311_IN(s(z0)) → c179(U54'(f323_in(z0), s(z0)), F323_IN(z0))
F331_IN(s(z0)) → c182(U55'(f194_in(z0), s(z0)), F194_IN(z0))
F15_IN(z0, z1) → c184(U56'(f21_in(z0, z1), f22_in(z0, z1), z0, z1), F21_IN(z0, z1))
F35_IN(z0, z1) → c187(U57'(f41_in(z0, z1), f42_in(z0, z1), z0, z1), F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(U58'(f59_in(z0, z1), f60_in(z0, z1), z0, z1), F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(U59'(f79_in(z0, z1), f80_in(z0, z1), z0, z1), F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(U60'(f99_in(z0, z1), f100_in(z0, z1), z0, z1), F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(U61'(f119_in(z0, z1), f120_in(z0, z1), z0, z1), F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(U62'(f139_in(z0, z1), f140_in(z0, z1), z0, z1), F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(U63'(f159_in(z0, z1), f161_in(z0, z1), z0, z1), F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(U64'(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2), F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(U65'(f210_in(z0), f212_in(z0), z0), F210_IN(z0))
F223_IN(z0) → c214(U66'(f230_in(z0), f232_in(z0), z0), F230_IN(z0))
F243_IN(z0) → c217(U67'(f250_in(z0), f252_in(z0), z0), F250_IN(z0))
F263_IN(z0) → c220(U68'(f271_in(z0), f272_in(z0), z0), F271_IN(z0))
F283_IN(z0) → c223(U69'(f291_in(z0), f292_in(z0), z0), F291_IN(z0))
F303_IN(z0) → c226(U70'(f311_in(z0), f312_in(z0), z0), F311_IN(z0))
F323_IN(z0) → c229(U71'(f331_in(z0), f332_in(z0), z0), F331_IN(z0))
F371_IN(z0) → c232(U72'(f379_in(z0), f380_in(z0), z0), F379_IN(z0))
F391_IN(z0) → c235(U73'(f399_in(z0), f400_in(z0), z0), F399_IN(z0))
F411_IN(z0) → c238(U74'(f419_in(z0), f420_in(z0), z0), F419_IN(z0))
F433_IN(z0) → c241(U75'(f439_in(z0), f440_in(z0), z0), F439_IN(z0))
F448_IN(z0) → c244(U76'(f457_in(z0), f458_in(z0), z0), F457_IN(z0))
F468_IN(z0) → c247(U77'(f477_in(z0), f478_in(z0), z0), F477_IN(z0))
F514_IN(z0) → c250(U78'(f523_in(z0), f524_in(z0), z0), F523_IN(z0))
F534_IN(z0) → c253(U79'(f543_in(z0), f544_in(z0), z0), F543_IN(z0))
F554_IN(z0) → c256(U80'(f563_in(z0), f564_in(z0), z0), F563_IN(z0))
F574_IN(z0) → c259(U81'(f583_in(z0), f584_in(z0), z0), F583_IN(z0))
F598_IN(z0) → c262(U82'(f605_in(z0), f606_in(z0), z0), F605_IN(z0))
F642_IN(z0) → c265(U83'(f649_in(z0), f650_in(z0), z0), F649_IN(z0))
F662_IN(z0) → c268(U84'(f669_in(z0), f670_in(z0), z0), F669_IN(z0))
F682_IN(z0) → c271(U85'(f689_in(z0), f690_in(z0), z0), F689_IN(z0))
F703_IN(z0) → c274(U86'(f709_in(z0), f710_in(z0), z0), F709_IN(z0))
F745_IN(z0) → c277(U87'(f751_in(z0), f752_in(z0), z0), F751_IN(z0))
F765_IN(z0) → c280(U88'(f771_in(z0), f772_in(z0), z0), F771_IN(z0))
F787_IN(z0) → c283(U89'(f793_in(z0), f794_in(z0), z0), F793_IN(z0))
F824_IN(z0) → c286(U90'(f829_in(z0), f830_in(z0), z0), F829_IN(z0))
F837_IN(z0) → c289(U91'(f841_in(z0), f842_in(z0), z0), F841_IN(z0))
F866_IN(z0) → c292(U92'(f870_in(z0), f871_in(z0), z0), F870_IN(z0))
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F1_IN, F860_IN, F816_IN, F167_IN, F736_IN, F7_IN, F633_IN, F507_IN, F363_IN, F194_IN, F21_IN, F41_IN, F42_IN, F59_IN, F60_IN, F870_IN, F79_IN, F80_IN, F829_IN, F99_IN, F100_IN, F751_IN, F841_IN, F119_IN, F120_IN, F649_IN, F771_IN, F139_IN, F140_IN, F523_IN, F669_IN, F793_IN, F159_IN, F161_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F15_IN, F35_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN

Compound Symbols:

c, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c46, c49, c52, c54, c57, c60, c63, c67, c70, c73, c76, c79, c82, c85, c89, c93, c96, c99, c103, c106, c108, c110, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c184, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292

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

Split RHS of tuples not part of any SCC

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F860_IN(z0) → c3(U2'(f866_in(z0), z0), F866_IN(z0))
F816_IN(z0) → c7(U3'(f824_in(z0), z0), F824_IN(z0))
F167_IN(z0, z1, z2) → c11(U4'(f174_in(z0, z1, z2), z0, z1, z2), F174_IN(z0, z1, z2))
F736_IN(z0) → c15(U5'(f745_in(z0), z0), F745_IN(z0))
F7_IN(z0, z1) → c19(U6'(f15_in(z0, z1), z0, z1), F15_IN(z0, z1))
F633_IN(z0) → c23(U7'(f642_in(z0), z0), F642_IN(z0))
F507_IN(z0) → c27(U8'(f514_in(z0), z0), F514_IN(z0))
F363_IN(z0) → c31(U9'(f371_in(z0), z0), F371_IN(z0))
F194_IN(z0) → c35(U10'(f202_in(z0), z0), F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(U11'(f35_in(z0, z1), s(z0), s(z1)), F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(U12'(f50_in(z0, z1), s(z0), s(z1)), F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(U14'(f70_in(z0, z1), s(z0), s(z1)), F70_IN(z0, z1))
F870_IN(s(z0)) → c54(U16'(f860_in(z0), s(z0)), F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(U17'(f91_in(z0, z1), s(z0), s(z1)), F91_IN(z0, z1))
F829_IN(s(z0)) → c63(U19'(f837_in(z0), s(z0)), F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(U20'(f110_in(z0, z1), s(z0), s(z1)), F110_IN(z0, z1))
F751_IN(s(z0)) → c73(U22'(f765_in(z0), s(z0)), F765_IN(z0))
F841_IN(s(z0)) → c76(U23'(f816_in(z0), s(z0)), F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(U24'(f131_in(z0, z1), s(z0), s(z1)), F131_IN(z0, z1))
F649_IN(s(z0)) → c85(U26'(f662_in(z0), s(z0)), F662_IN(z0))
F771_IN(s(z0)) → c89(U27'(f787_in(z0), s(z0)), F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(U28'(f151_in(z0, z1), s(z0), s(z1)), F151_IN(z0, z1))
F523_IN(s(z0)) → c99(U30'(f534_in(z0), s(z0)), F534_IN(z0))
F669_IN(s(z0)) → c103(U31'(f682_in(z0), s(z0)), F682_IN(z0))
F793_IN(s(z0)) → c106(U32'(f736_in(z0), s(z0)), F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(U33'(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1)), F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(U35'(f391_in(z0), s(z0)), F391_IN(z0))
F543_IN(s(z0)) → c117(U36'(f554_in(z0), s(z0)), F554_IN(z0))
F689_IN(s(z0)) → c121(U37'(f703_in(z0), s(z0)), F703_IN(z0))
F210_IN(s(z0)) → c125(U38'(f223_in(z0), s(z0)), F223_IN(z0))
F399_IN(s(z0)) → c129(U39'(f411_in(z0), s(z0)), F411_IN(z0))
F563_IN(s(z0)) → c133(U40'(f574_in(z0), s(z0)), F574_IN(z0))
F709_IN(s(z0)) → c136(U41'(f633_in(z0), s(z0)), F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(U42'(f167_in(z0, z1, z2), s(z0), s(z1), z2), F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(U43'(f7_in(z0, s(z1)), z0, 0, z1), F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(U44'(f243_in(z0), s(z0)), F243_IN(z0))
F419_IN(s(z0)) → c147(U45'(f433_in(z0), s(z0)), F433_IN(z0))
F583_IN(s(z0)) → c151(U46'(f598_in(z0), s(z0)), F598_IN(z0))
F250_IN(s(z0)) → c155(U47'(f263_in(z0), s(z0)), F263_IN(z0))
F439_IN(s(z0)) → c159(U48'(f448_in(z0), s(z0)), F448_IN(z0))
F605_IN(s(z0)) → c162(U49'(f507_in(z0), s(z0)), F507_IN(z0))
F271_IN(s(z0)) → c165(U50'(f283_in(z0), s(z0)), F283_IN(z0))
F457_IN(s(z0)) → c169(U51'(f468_in(z0), s(z0)), F468_IN(z0))
F291_IN(s(z0)) → c173(U52'(f303_in(z0), s(z0)), F303_IN(z0))
F477_IN(s(z0)) → c176(U53'(f363_in(z0), s(z0)), F363_IN(z0))
F311_IN(s(z0)) → c179(U54'(f323_in(z0), s(z0)), F323_IN(z0))
F331_IN(s(z0)) → c182(U55'(f194_in(z0), s(z0)), F194_IN(z0))
F15_IN(z0, z1) → c184(U56'(f21_in(z0, z1), f22_in(z0, z1), z0, z1), F21_IN(z0, z1))
F35_IN(z0, z1) → c187(U57'(f41_in(z0, z1), f42_in(z0, z1), z0, z1), F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(U58'(f59_in(z0, z1), f60_in(z0, z1), z0, z1), F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(U59'(f79_in(z0, z1), f80_in(z0, z1), z0, z1), F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(U60'(f99_in(z0, z1), f100_in(z0, z1), z0, z1), F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(U61'(f119_in(z0, z1), f120_in(z0, z1), z0, z1), F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(U62'(f139_in(z0, z1), f140_in(z0, z1), z0, z1), F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(U63'(f159_in(z0, z1), f161_in(z0, z1), z0, z1), F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(U64'(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2), F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(U65'(f210_in(z0), f212_in(z0), z0), F210_IN(z0))
F223_IN(z0) → c214(U66'(f230_in(z0), f232_in(z0), z0), F230_IN(z0))
F243_IN(z0) → c217(U67'(f250_in(z0), f252_in(z0), z0), F250_IN(z0))
F263_IN(z0) → c220(U68'(f271_in(z0), f272_in(z0), z0), F271_IN(z0))
F283_IN(z0) → c223(U69'(f291_in(z0), f292_in(z0), z0), F291_IN(z0))
F303_IN(z0) → c226(U70'(f311_in(z0), f312_in(z0), z0), F311_IN(z0))
F323_IN(z0) → c229(U71'(f331_in(z0), f332_in(z0), z0), F331_IN(z0))
F371_IN(z0) → c232(U72'(f379_in(z0), f380_in(z0), z0), F379_IN(z0))
F391_IN(z0) → c235(U73'(f399_in(z0), f400_in(z0), z0), F399_IN(z0))
F411_IN(z0) → c238(U74'(f419_in(z0), f420_in(z0), z0), F419_IN(z0))
F433_IN(z0) → c241(U75'(f439_in(z0), f440_in(z0), z0), F439_IN(z0))
F448_IN(z0) → c244(U76'(f457_in(z0), f458_in(z0), z0), F457_IN(z0))
F468_IN(z0) → c247(U77'(f477_in(z0), f478_in(z0), z0), F477_IN(z0))
F514_IN(z0) → c250(U78'(f523_in(z0), f524_in(z0), z0), F523_IN(z0))
F534_IN(z0) → c253(U79'(f543_in(z0), f544_in(z0), z0), F543_IN(z0))
F554_IN(z0) → c256(U80'(f563_in(z0), f564_in(z0), z0), F563_IN(z0))
F574_IN(z0) → c259(U81'(f583_in(z0), f584_in(z0), z0), F583_IN(z0))
F598_IN(z0) → c262(U82'(f605_in(z0), f606_in(z0), z0), F605_IN(z0))
F642_IN(z0) → c265(U83'(f649_in(z0), f650_in(z0), z0), F649_IN(z0))
F662_IN(z0) → c268(U84'(f669_in(z0), f670_in(z0), z0), F669_IN(z0))
F682_IN(z0) → c271(U85'(f689_in(z0), f690_in(z0), z0), F689_IN(z0))
F703_IN(z0) → c274(U86'(f709_in(z0), f710_in(z0), z0), F709_IN(z0))
F745_IN(z0) → c277(U87'(f751_in(z0), f752_in(z0), z0), F751_IN(z0))
F765_IN(z0) → c280(U88'(f771_in(z0), f772_in(z0), z0), F771_IN(z0))
F787_IN(z0) → c283(U89'(f793_in(z0), f794_in(z0), z0), F793_IN(z0))
F824_IN(z0) → c286(U90'(f829_in(z0), f830_in(z0), z0), F829_IN(z0))
F837_IN(z0) → c289(U91'(f841_in(z0), f842_in(z0), z0), F841_IN(z0))
F866_IN(z0) → c292(U92'(f870_in(z0), f871_in(z0), z0), F870_IN(z0))
F1_IN(z0, z1) → c1(U1'(f7_in(z0, z1), z0, z1))
F1_IN(z0, z1) → c1(F7_IN(z0, z1))
F42_IN(z0, 0) → c1(U13'(f860_in(z0), z0, 0))
F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(U15'(f816_in(z0), z0, 0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(U18'(f736_in(z0), z0, 0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(U21'(f633_in(z0), z0, 0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(U25'(f507_in(z0), z0, 0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(U29'(f363_in(z0), z0, 0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(U34'(f194_in(z0), z0, 0))
F161_IN(z0, 0) → c1(F194_IN(z0))
S tuples:

F860_IN(z0) → c3(U2'(f866_in(z0), z0), F866_IN(z0))
F816_IN(z0) → c7(U3'(f824_in(z0), z0), F824_IN(z0))
F167_IN(z0, z1, z2) → c11(U4'(f174_in(z0, z1, z2), z0, z1, z2), F174_IN(z0, z1, z2))
F736_IN(z0) → c15(U5'(f745_in(z0), z0), F745_IN(z0))
F7_IN(z0, z1) → c19(U6'(f15_in(z0, z1), z0, z1), F15_IN(z0, z1))
F633_IN(z0) → c23(U7'(f642_in(z0), z0), F642_IN(z0))
F507_IN(z0) → c27(U8'(f514_in(z0), z0), F514_IN(z0))
F363_IN(z0) → c31(U9'(f371_in(z0), z0), F371_IN(z0))
F194_IN(z0) → c35(U10'(f202_in(z0), z0), F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(U11'(f35_in(z0, z1), s(z0), s(z1)), F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(U12'(f50_in(z0, z1), s(z0), s(z1)), F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(U14'(f70_in(z0, z1), s(z0), s(z1)), F70_IN(z0, z1))
F870_IN(s(z0)) → c54(U16'(f860_in(z0), s(z0)), F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(U17'(f91_in(z0, z1), s(z0), s(z1)), F91_IN(z0, z1))
F829_IN(s(z0)) → c63(U19'(f837_in(z0), s(z0)), F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(U20'(f110_in(z0, z1), s(z0), s(z1)), F110_IN(z0, z1))
F751_IN(s(z0)) → c73(U22'(f765_in(z0), s(z0)), F765_IN(z0))
F841_IN(s(z0)) → c76(U23'(f816_in(z0), s(z0)), F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(U24'(f131_in(z0, z1), s(z0), s(z1)), F131_IN(z0, z1))
F649_IN(s(z0)) → c85(U26'(f662_in(z0), s(z0)), F662_IN(z0))
F771_IN(s(z0)) → c89(U27'(f787_in(z0), s(z0)), F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(U28'(f151_in(z0, z1), s(z0), s(z1)), F151_IN(z0, z1))
F523_IN(s(z0)) → c99(U30'(f534_in(z0), s(z0)), F534_IN(z0))
F669_IN(s(z0)) → c103(U31'(f682_in(z0), s(z0)), F682_IN(z0))
F793_IN(s(z0)) → c106(U32'(f736_in(z0), s(z0)), F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(U33'(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1)), F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(U35'(f391_in(z0), s(z0)), F391_IN(z0))
F543_IN(s(z0)) → c117(U36'(f554_in(z0), s(z0)), F554_IN(z0))
F689_IN(s(z0)) → c121(U37'(f703_in(z0), s(z0)), F703_IN(z0))
F210_IN(s(z0)) → c125(U38'(f223_in(z0), s(z0)), F223_IN(z0))
F399_IN(s(z0)) → c129(U39'(f411_in(z0), s(z0)), F411_IN(z0))
F563_IN(s(z0)) → c133(U40'(f574_in(z0), s(z0)), F574_IN(z0))
F709_IN(s(z0)) → c136(U41'(f633_in(z0), s(z0)), F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(U42'(f167_in(z0, z1, z2), s(z0), s(z1), z2), F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(U43'(f7_in(z0, s(z1)), z0, 0, z1), F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(U44'(f243_in(z0), s(z0)), F243_IN(z0))
F419_IN(s(z0)) → c147(U45'(f433_in(z0), s(z0)), F433_IN(z0))
F583_IN(s(z0)) → c151(U46'(f598_in(z0), s(z0)), F598_IN(z0))
F250_IN(s(z0)) → c155(U47'(f263_in(z0), s(z0)), F263_IN(z0))
F439_IN(s(z0)) → c159(U48'(f448_in(z0), s(z0)), F448_IN(z0))
F605_IN(s(z0)) → c162(U49'(f507_in(z0), s(z0)), F507_IN(z0))
F271_IN(s(z0)) → c165(U50'(f283_in(z0), s(z0)), F283_IN(z0))
F457_IN(s(z0)) → c169(U51'(f468_in(z0), s(z0)), F468_IN(z0))
F291_IN(s(z0)) → c173(U52'(f303_in(z0), s(z0)), F303_IN(z0))
F477_IN(s(z0)) → c176(U53'(f363_in(z0), s(z0)), F363_IN(z0))
F311_IN(s(z0)) → c179(U54'(f323_in(z0), s(z0)), F323_IN(z0))
F331_IN(s(z0)) → c182(U55'(f194_in(z0), s(z0)), F194_IN(z0))
F15_IN(z0, z1) → c184(U56'(f21_in(z0, z1), f22_in(z0, z1), z0, z1), F21_IN(z0, z1))
F35_IN(z0, z1) → c187(U57'(f41_in(z0, z1), f42_in(z0, z1), z0, z1), F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(U58'(f59_in(z0, z1), f60_in(z0, z1), z0, z1), F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(U59'(f79_in(z0, z1), f80_in(z0, z1), z0, z1), F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(U60'(f99_in(z0, z1), f100_in(z0, z1), z0, z1), F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(U61'(f119_in(z0, z1), f120_in(z0, z1), z0, z1), F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(U62'(f139_in(z0, z1), f140_in(z0, z1), z0, z1), F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(U63'(f159_in(z0, z1), f161_in(z0, z1), z0, z1), F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(U64'(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2), F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(U65'(f210_in(z0), f212_in(z0), z0), F210_IN(z0))
F223_IN(z0) → c214(U66'(f230_in(z0), f232_in(z0), z0), F230_IN(z0))
F243_IN(z0) → c217(U67'(f250_in(z0), f252_in(z0), z0), F250_IN(z0))
F263_IN(z0) → c220(U68'(f271_in(z0), f272_in(z0), z0), F271_IN(z0))
F283_IN(z0) → c223(U69'(f291_in(z0), f292_in(z0), z0), F291_IN(z0))
F303_IN(z0) → c226(U70'(f311_in(z0), f312_in(z0), z0), F311_IN(z0))
F323_IN(z0) → c229(U71'(f331_in(z0), f332_in(z0), z0), F331_IN(z0))
F371_IN(z0) → c232(U72'(f379_in(z0), f380_in(z0), z0), F379_IN(z0))
F391_IN(z0) → c235(U73'(f399_in(z0), f400_in(z0), z0), F399_IN(z0))
F411_IN(z0) → c238(U74'(f419_in(z0), f420_in(z0), z0), F419_IN(z0))
F433_IN(z0) → c241(U75'(f439_in(z0), f440_in(z0), z0), F439_IN(z0))
F448_IN(z0) → c244(U76'(f457_in(z0), f458_in(z0), z0), F457_IN(z0))
F468_IN(z0) → c247(U77'(f477_in(z0), f478_in(z0), z0), F477_IN(z0))
F514_IN(z0) → c250(U78'(f523_in(z0), f524_in(z0), z0), F523_IN(z0))
F534_IN(z0) → c253(U79'(f543_in(z0), f544_in(z0), z0), F543_IN(z0))
F554_IN(z0) → c256(U80'(f563_in(z0), f564_in(z0), z0), F563_IN(z0))
F574_IN(z0) → c259(U81'(f583_in(z0), f584_in(z0), z0), F583_IN(z0))
F598_IN(z0) → c262(U82'(f605_in(z0), f606_in(z0), z0), F605_IN(z0))
F642_IN(z0) → c265(U83'(f649_in(z0), f650_in(z0), z0), F649_IN(z0))
F662_IN(z0) → c268(U84'(f669_in(z0), f670_in(z0), z0), F669_IN(z0))
F682_IN(z0) → c271(U85'(f689_in(z0), f690_in(z0), z0), F689_IN(z0))
F703_IN(z0) → c274(U86'(f709_in(z0), f710_in(z0), z0), F709_IN(z0))
F745_IN(z0) → c277(U87'(f751_in(z0), f752_in(z0), z0), F751_IN(z0))
F765_IN(z0) → c280(U88'(f771_in(z0), f772_in(z0), z0), F771_IN(z0))
F787_IN(z0) → c283(U89'(f793_in(z0), f794_in(z0), z0), F793_IN(z0))
F824_IN(z0) → c286(U90'(f829_in(z0), f830_in(z0), z0), F829_IN(z0))
F837_IN(z0) → c289(U91'(f841_in(z0), f842_in(z0), z0), F841_IN(z0))
F866_IN(z0) → c292(U92'(f870_in(z0), f871_in(z0), z0), F870_IN(z0))
F1_IN(z0, z1) → c1(U1'(f7_in(z0, z1), z0, z1))
F1_IN(z0, z1) → c1(F7_IN(z0, z1))
F42_IN(z0, 0) → c1(U13'(f860_in(z0), z0, 0))
F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(U15'(f816_in(z0), z0, 0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(U18'(f736_in(z0), z0, 0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(U21'(f633_in(z0), z0, 0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(U25'(f507_in(z0), z0, 0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(U29'(f363_in(z0), z0, 0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(U34'(f194_in(z0), z0, 0))
F161_IN(z0, 0) → c1(F194_IN(z0))
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F860_IN, F816_IN, F167_IN, F736_IN, F7_IN, F633_IN, F507_IN, F363_IN, F194_IN, F21_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F15_IN, F35_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F1_IN, F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN

Compound Symbols:

c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c184, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c1

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

Removed 92 trailing tuple parts

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F1_IN(z0, z1) → c1(F7_IN(z0, z1))
F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F7_IN(z0, z1) → c19(F15_IN(z0, z1))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F15_IN(z0, z1) → c184(F21_IN(z0, z1))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F1_IN(z0, z1) → c1
F42_IN(z0, 0) → c1
F60_IN(z0, 0) → c1
F80_IN(z0, 0) → c1
F100_IN(z0, 0) → c1
F120_IN(z0, 0) → c1
F140_IN(z0, 0) → c1
F161_IN(z0, 0) → c1
S tuples:

F1_IN(z0, z1) → c1(F7_IN(z0, z1))
F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F7_IN(z0, z1) → c19(F15_IN(z0, z1))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F15_IN(z0, z1) → c184(F21_IN(z0, z1))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F1_IN(z0, z1) → c1
F42_IN(z0, 0) → c1
F60_IN(z0, 0) → c1
F80_IN(z0, 0) → c1
F100_IN(z0, 0) → c1
F120_IN(z0, 0) → c1
F140_IN(z0, 0) → c1
F161_IN(z0, 0) → c1
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F1_IN, F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F7_IN, F633_IN, F507_IN, F363_IN, F194_IN, F21_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F15_IN, F35_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN

Compound Symbols:

c1, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c184, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c1

(9) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

F1_IN(z0, z1) → c1(F7_IN(z0, z1))
F1_IN(z0, z1) → c1

(10) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F1_IN(z0, z1) → c1(F7_IN(z0, z1))
F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F7_IN(z0, z1) → c19(F15_IN(z0, z1))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F15_IN(z0, z1) → c184(F21_IN(z0, z1))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F1_IN(z0, z1) → c1
F42_IN(z0, 0) → c1
F60_IN(z0, 0) → c1
F80_IN(z0, 0) → c1
F100_IN(z0, 0) → c1
F120_IN(z0, 0) → c1
F140_IN(z0, 0) → c1
F161_IN(z0, 0) → c1
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F7_IN(z0, z1) → c19(F15_IN(z0, z1))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F15_IN(z0, z1) → c184(F21_IN(z0, z1))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F42_IN(z0, 0) → c1
F60_IN(z0, 0) → c1
F80_IN(z0, 0) → c1
F100_IN(z0, 0) → c1
F120_IN(z0, 0) → c1
F140_IN(z0, 0) → c1
F161_IN(z0, 0) → c1
K tuples:

F1_IN(z0, z1) → c1(F7_IN(z0, z1))
F1_IN(z0, z1) → c1
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F1_IN, F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F7_IN, F633_IN, F507_IN, F363_IN, F194_IN, F21_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F15_IN, F35_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN

Compound Symbols:

c1, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c184, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c1

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

Use forward instantiation to replace F15_IN(z0, z1) → c184(F21_IN(z0, z1)) by

F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F1_IN(z0, z1) → c1(F7_IN(z0, z1))
F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F7_IN(z0, z1) → c19(F15_IN(z0, z1))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F1_IN(z0, z1) → c1
F42_IN(z0, 0) → c1
F60_IN(z0, 0) → c1
F80_IN(z0, 0) → c1
F100_IN(z0, 0) → c1
F120_IN(z0, 0) → c1
F140_IN(z0, 0) → c1
F161_IN(z0, 0) → c1
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F7_IN(z0, z1) → c19(F15_IN(z0, z1))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F42_IN(z0, 0) → c1
F60_IN(z0, 0) → c1
F80_IN(z0, 0) → c1
F100_IN(z0, 0) → c1
F120_IN(z0, 0) → c1
F140_IN(z0, 0) → c1
F161_IN(z0, 0) → c1
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
K tuples:

F1_IN(z0, z1) → c1(F7_IN(z0, z1))
F1_IN(z0, z1) → c1
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F1_IN, F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F7_IN, F633_IN, F507_IN, F363_IN, F194_IN, F21_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F35_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN

Compound Symbols:

c1, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c1, c184

(13) CdtGraphRemoveDanglingProof (ComplexityIfPolyImplication transformation)

Removed 2 of 100 dangling nodes:

F1_IN(z0, z1) → c1(F7_IN(z0, z1))
F1_IN(z0, z1) → c1

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F7_IN(z0, z1) → c19(F15_IN(z0, z1))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F42_IN(z0, 0) → c1
F60_IN(z0, 0) → c1
F80_IN(z0, 0) → c1
F100_IN(z0, 0) → c1
F120_IN(z0, 0) → c1
F140_IN(z0, 0) → c1
F161_IN(z0, 0) → c1
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F7_IN(z0, z1) → c19(F15_IN(z0, z1))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F42_IN(z0, 0) → c1
F60_IN(z0, 0) → c1
F80_IN(z0, 0) → c1
F100_IN(z0, 0) → c1
F120_IN(z0, 0) → c1
F140_IN(z0, 0) → c1
F161_IN(z0, 0) → c1
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F7_IN, F633_IN, F507_IN, F363_IN, F194_IN, F21_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F35_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN

Compound Symbols:

c1, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c1, c184

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

Split RHS of tuples not part of any SCC

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F7_IN(z0, z1) → c19(F15_IN(z0, z1))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F7_IN(z0, z1) → c19(F15_IN(z0, z1))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F7_IN, F633_IN, F507_IN, F363_IN, F194_IN, F21_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F35_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN

Compound Symbols:

c1, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184

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

Use instantiation to replace F7_IN(z0, z1) → c19(F15_IN(z0, z1)) by

F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))

(18) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F633_IN, F507_IN, F363_IN, F194_IN, F21_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F35_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN, F7_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19

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

Use forward instantiation to replace F35_IN(z0, z1) → c187(F41_IN(z0, z1), F42_IN(z0, z1)) by

F35_IN(z0, 0) → c187(F41_IN(z0, 0), F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)), F42_IN(s(y0), s(y1)))

(20) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c187(F41_IN(z0, 0), F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)), F42_IN(s(y0), s(y1)))
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c187(F41_IN(z0, 0), F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)), F42_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F633_IN, F507_IN, F363_IN, F194_IN, F21_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN, F7_IN, F35_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c187

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

Split RHS of tuples not part of any SCC

(22) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)), F42_IN(s(y0), s(y1)))
F35_IN(z0, 0) → c(F41_IN(z0, 0))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)), F42_IN(s(y0), s(y1)))
F35_IN(z0, 0) → c(F41_IN(z0, 0))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F633_IN, F507_IN, F363_IN, F194_IN, F21_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN, F7_IN, F35_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c187, c

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

Removed 2 trailing tuple parts

(24) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F35_IN(z0, 0) → c
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F35_IN(z0, 0) → c
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F633_IN, F507_IN, F363_IN, F194_IN, F21_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN, F7_IN, F35_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c, c187, c

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

Use forward instantiation to replace F21_IN(s(z0), s(z1)) → c39(F35_IN(z0, z1)) by

F21_IN(s(z0), s(0)) → c39(F35_IN(z0, 0))
F21_IN(s(s(y0)), s(s(y1))) → c39(F35_IN(s(y0), s(y1)))

(26) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F35_IN(z0, 0) → c
F21_IN(s(z0), s(0)) → c39(F35_IN(z0, 0))
F21_IN(s(s(y0)), s(s(y1))) → c39(F35_IN(s(y0), s(y1)))
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F35_IN(z0, 0) → c
F21_IN(s(z0), s(0)) → c39(F35_IN(z0, 0))
F21_IN(s(s(y0)), s(s(y1))) → c39(F35_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F633_IN, F507_IN, F363_IN, F194_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN, F7_IN, F35_IN, F21_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c, c187, c, c39

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

Split RHS of tuples not part of any SCC

(28) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F21_IN(s(z0), s(0)) → c39(F35_IN(z0, 0))
F21_IN(s(s(y0)), s(s(y1))) → c39(F35_IN(s(y0), s(y1)))
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F21_IN(s(z0), s(0)) → c39(F35_IN(z0, 0))
F21_IN(s(s(y0)), s(s(y1))) → c39(F35_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F633_IN, F507_IN, F363_IN, F194_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F50_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN, F7_IN, F35_IN, F21_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c, c187, c39

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

Use forward instantiation to replace F50_IN(z0, z1) → c190(F59_IN(z0, z1), F60_IN(z0, z1)) by

F50_IN(z0, 0) → c190(F59_IN(z0, 0), F60_IN(z0, 0))
F50_IN(s(y0), s(y1)) → c190(F59_IN(s(y0), s(y1)), F60_IN(s(y0), s(y1)))

(30) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F21_IN(s(z0), s(0)) → c39(F35_IN(z0, 0))
F21_IN(s(s(y0)), s(s(y1))) → c39(F35_IN(s(y0), s(y1)))
F50_IN(z0, 0) → c190(F59_IN(z0, 0), F60_IN(z0, 0))
F50_IN(s(y0), s(y1)) → c190(F59_IN(s(y0), s(y1)), F60_IN(s(y0), s(y1)))
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F21_IN(s(z0), s(0)) → c39(F35_IN(z0, 0))
F21_IN(s(s(y0)), s(s(y1))) → c39(F35_IN(s(y0), s(y1)))
F50_IN(z0, 0) → c190(F59_IN(z0, 0), F60_IN(z0, 0))
F50_IN(s(y0), s(y1)) → c190(F59_IN(s(y0), s(y1)), F60_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F633_IN, F507_IN, F363_IN, F194_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN, F7_IN, F35_IN, F21_IN, F50_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c, c187, c39, c190

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

Split RHS of tuples not part of any SCC

(32) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F21_IN(s(z0), s(0)) → c39(F35_IN(z0, 0))
F21_IN(s(s(y0)), s(s(y1))) → c39(F35_IN(s(y0), s(y1)))
F50_IN(s(y0), s(y1)) → c190(F59_IN(s(y0), s(y1)), F60_IN(s(y0), s(y1)))
F50_IN(z0, 0) → c2(F59_IN(z0, 0))
F50_IN(z0, 0) → c2(F60_IN(z0, 0))
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F21_IN(s(z0), s(0)) → c39(F35_IN(z0, 0))
F21_IN(s(s(y0)), s(s(y1))) → c39(F35_IN(s(y0), s(y1)))
F50_IN(s(y0), s(y1)) → c190(F59_IN(s(y0), s(y1)), F60_IN(s(y0), s(y1)))
F50_IN(z0, 0) → c2(F59_IN(z0, 0))
F50_IN(z0, 0) → c2(F60_IN(z0, 0))
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F633_IN, F507_IN, F363_IN, F194_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN, F7_IN, F35_IN, F21_IN, F50_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c, c187, c39, c190, c2

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

Removed 2 trailing tuple parts

(34) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0, z1) → U1(f7_in(z0, z1), z0, z1)
U1(f7_out1(z0), z1, z2) → f1_out1(z0)
f860_in(0) → f860_out1(0)
f860_in(z0) → U2(f866_in(z0), z0)
U2(f866_out1(z0), z1) → f860_out1(z0)
U2(f866_out2(z0), z1) → f860_out1(z0)
f816_in(0) → f816_out1(0)
f816_in(z0) → U3(f824_in(z0), z0)
U3(f824_out1(z0), z1) → f816_out1(z0)
U3(f824_out2(z0), z1) → f816_out1(z0)
f167_in(0, s(z0), z1) → f167_out1(0)
f167_in(z0, z1, z2) → U4(f174_in(z0, z1, z2), z0, z1, z2)
U4(f174_out1(z0), z1, z2, z3) → f167_out1(z0)
U4(f174_out2(z0), z1, z2, z3) → f167_out1(z0)
f736_in(0) → f736_out1(0)
f736_in(z0) → U5(f745_in(z0), z0)
U5(f745_out1(z0), z1) → f736_out1(z0)
U5(f745_out2(z0), z1) → f736_out1(z0)
f7_in(0, s(z0)) → f7_out1(0)
f7_in(z0, z1) → U6(f15_in(z0, z1), z0, z1)
U6(f15_out1(z0), z1, z2) → f7_out1(z0)
U6(f15_out2(z0), z1, z2) → f7_out1(z0)
f633_in(0) → f633_out1(0)
f633_in(z0) → U7(f642_in(z0), z0)
U7(f642_out1(z0), z1) → f633_out1(z0)
U7(f642_out2(z0), z1) → f633_out1(z0)
f507_in(0) → f507_out1(0)
f507_in(z0) → U8(f514_in(z0), z0)
U8(f514_out1(z0), z1) → f507_out1(z0)
U8(f514_out2(z0), z1) → f507_out1(z0)
f363_in(0) → f363_out1(0)
f363_in(z0) → U9(f371_in(z0), z0)
U9(f371_out1(z0), z1) → f363_out1(z0)
U9(f371_out2(z0), z1) → f363_out1(z0)
f194_in(0) → f194_out1(0)
f194_in(z0) → U10(f202_in(z0), z0)
U10(f202_out1(z0), z1) → f194_out1(z0)
U10(f202_out2(z0), z1) → f194_out1(z0)
f21_in(s(0), s(s(z0))) → f21_out1(0)
f21_in(s(z0), s(z1)) → U11(f35_in(z0, z1), s(z0), s(z1))
U11(f35_out1(z0), s(z1), s(z2)) → f21_out1(z0)
U11(f35_out2(z0), s(z1), s(z2)) → f21_out1(z0)
f41_in(s(0), s(s(z0))) → f41_out1(0)
f41_in(s(z0), s(z1)) → U12(f50_in(z0, z1), s(z0), s(z1))
U12(f50_out1(z0), s(z1), s(z2)) → f41_out1(z0)
U12(f50_out2(z0), s(z1), s(z2)) → f41_out1(z0)
f42_in(z0, 0) → U13(f860_in(z0), z0, 0)
U13(f860_out1(z0), z1, 0) → f42_out1(s(z0))
f59_in(s(0), s(s(z0))) → f59_out1(0)
f59_in(s(z0), s(z1)) → U14(f70_in(z0, z1), s(z0), s(z1))
U14(f70_out1(z0), s(z1), s(z2)) → f59_out1(z0)
U14(f70_out2(z0), s(z1), s(z2)) → f59_out1(z0)
f60_in(z0, 0) → U15(f816_in(z0), z0, 0)
U15(f816_out1(z0), z1, 0) → f60_out1(s(z0))
f870_in(s(z0)) → U16(f860_in(z0), s(z0))
U16(f860_out1(z0), s(z1)) → f870_out1(s(z0))
f79_in(s(0), s(s(z0))) → f79_out1(0)
f79_in(s(z0), s(z1)) → U17(f91_in(z0, z1), s(z0), s(z1))
U17(f91_out1(z0), s(z1), s(z2)) → f79_out1(z0)
U17(f91_out2(z0), s(z1), s(z2)) → f79_out1(z0)
f80_in(z0, 0) → U18(f736_in(z0), z0, 0)
U18(f736_out1(z0), z1, 0) → f80_out1(s(z0))
f829_in(s(0)) → f829_out1(0)
f829_in(s(z0)) → U19(f837_in(z0), s(z0))
U19(f837_out1(z0), s(z1)) → f829_out1(z0)
U19(f837_out2(z0), s(z1)) → f829_out1(z0)
f99_in(s(0), s(s(z0))) → f99_out1(0)
f99_in(s(z0), s(z1)) → U20(f110_in(z0, z1), s(z0), s(z1))
U20(f110_out1(z0), s(z1), s(z2)) → f99_out1(z0)
U20(f110_out2(z0), s(z1), s(z2)) → f99_out1(z0)
f100_in(z0, 0) → U21(f633_in(z0), z0, 0)
U21(f633_out1(z0), z1, 0) → f100_out1(s(z0))
f751_in(s(0)) → f751_out1(0)
f751_in(s(z0)) → U22(f765_in(z0), s(z0))
U22(f765_out1(z0), s(z1)) → f751_out1(z0)
U22(f765_out2(z0), s(z1)) → f751_out1(z0)
f841_in(s(z0)) → U23(f816_in(z0), s(z0))
U23(f816_out1(z0), s(z1)) → f841_out1(s(z0))
f119_in(s(0), s(s(z0))) → f119_out1(0)
f119_in(s(z0), s(z1)) → U24(f131_in(z0, z1), s(z0), s(z1))
U24(f131_out1(z0), s(z1), s(z2)) → f119_out1(z0)
U24(f131_out2(z0), s(z1), s(z2)) → f119_out1(z0)
f120_in(z0, 0) → U25(f507_in(z0), z0, 0)
U25(f507_out1(z0), z1, 0) → f120_out1(s(z0))
f649_in(s(0)) → f649_out1(0)
f649_in(s(z0)) → U26(f662_in(z0), s(z0))
U26(f662_out1(z0), s(z1)) → f649_out1(z0)
U26(f662_out2(z0), s(z1)) → f649_out1(z0)
f771_in(s(0)) → f771_out1(0)
f771_in(s(z0)) → U27(f787_in(z0), s(z0))
U27(f787_out1(z0), s(z1)) → f771_out1(z0)
U27(f787_out2(z0), s(z1)) → f771_out1(z0)
f139_in(s(0), s(s(z0))) → f139_out1(0)
f139_in(s(z0), s(z1)) → U28(f151_in(z0, z1), s(z0), s(z1))
U28(f151_out1(z0), s(z1), s(z2)) → f139_out1(z0)
U28(f151_out2(z0), s(z1), s(z2)) → f139_out1(z0)
f140_in(z0, 0) → U29(f363_in(z0), z0, 0)
U29(f363_out1(z0), z1, 0) → f140_out1(s(z0))
f523_in(s(0)) → f523_out1(0)
f523_in(s(z0)) → U30(f534_in(z0), s(z0))
U30(f534_out1(z0), s(z1)) → f523_out1(z0)
U30(f534_out2(z0), s(z1)) → f523_out1(z0)
f669_in(s(0)) → f669_out1(0)
f669_in(s(z0)) → U31(f682_in(z0), s(z0))
U31(f682_out1(z0), s(z1)) → f669_out1(z0)
U31(f682_out2(z0), s(z1)) → f669_out1(z0)
f793_in(s(z0)) → U32(f736_in(z0), s(z0))
U32(f736_out1(z0), s(z1)) → f793_out1(s(z0))
f159_in(s(z0), s(z1)) → U33(f167_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f167_out1(z0), s(z1), s(z2)) → f159_out1(z0)
f161_in(z0, 0) → U34(f194_in(z0), z0, 0)
U34(f194_out1(z0), z1, 0) → f161_out1(s(z0))
f379_in(s(0)) → f379_out1(0)
f379_in(s(z0)) → U35(f391_in(z0), s(z0))
U35(f391_out1(z0), s(z1)) → f379_out1(z0)
U35(f391_out2(z0), s(z1)) → f379_out1(z0)
f543_in(s(0)) → f543_out1(0)
f543_in(s(z0)) → U36(f554_in(z0), s(z0))
U36(f554_out1(z0), s(z1)) → f543_out1(z0)
U36(f554_out2(z0), s(z1)) → f543_out1(z0)
f689_in(s(0)) → f689_out1(0)
f689_in(s(z0)) → U37(f703_in(z0), s(z0))
U37(f703_out1(z0), s(z1)) → f689_out1(z0)
U37(f703_out2(z0), s(z1)) → f689_out1(z0)
f210_in(s(0)) → f210_out1(0)
f210_in(s(z0)) → U38(f223_in(z0), s(z0))
U38(f223_out1(z0), s(z1)) → f210_out1(z0)
U38(f223_out2(z0), s(z1)) → f210_out1(z0)
f399_in(s(0)) → f399_out1(0)
f399_in(s(z0)) → U39(f411_in(z0), s(z0))
U39(f411_out1(z0), s(z1)) → f399_out1(z0)
U39(f411_out2(z0), s(z1)) → f399_out1(z0)
f563_in(s(0)) → f563_out1(0)
f563_in(s(z0)) → U40(f574_in(z0), s(z0))
U40(f574_out1(z0), s(z1)) → f563_out1(z0)
U40(f574_out2(z0), s(z1)) → f563_out1(z0)
f709_in(s(z0)) → U41(f633_in(z0), s(z0))
U41(f633_out1(z0), s(z1)) → f709_out1(s(z0))
f182_in(s(z0), s(z1), z2) → U42(f167_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f167_out1(z0), s(z1), s(z2), z3) → f182_out1(z0)
f184_in(z0, 0, z1) → U43(f7_in(z0, s(z1)), z0, 0, z1)
U43(f7_out1(z0), z1, 0, z2) → f184_out1(s(z0))
f230_in(s(0)) → f230_out1(0)
f230_in(s(z0)) → U44(f243_in(z0), s(z0))
U44(f243_out1(z0), s(z1)) → f230_out1(z0)
U44(f243_out2(z0), s(z1)) → f230_out1(z0)
f419_in(s(0)) → f419_out1(0)
f419_in(s(z0)) → U45(f433_in(z0), s(z0))
U45(f433_out1(z0), s(z1)) → f419_out1(z0)
U45(f433_out2(z0), s(z1)) → f419_out1(z0)
f583_in(s(0)) → f583_out1(0)
f583_in(s(z0)) → U46(f598_in(z0), s(z0))
U46(f598_out1(z0), s(z1)) → f583_out1(z0)
U46(f598_out2(z0), s(z1)) → f583_out1(z0)
f250_in(s(0)) → f250_out1(0)
f250_in(s(z0)) → U47(f263_in(z0), s(z0))
U47(f263_out1(z0), s(z1)) → f250_out1(z0)
U47(f263_out2(z0), s(z1)) → f250_out1(z0)
f439_in(s(0)) → f439_out1(0)
f439_in(s(z0)) → U48(f448_in(z0), s(z0))
U48(f448_out1(z0), s(z1)) → f439_out1(z0)
U48(f448_out2(z0), s(z1)) → f439_out1(z0)
f605_in(s(z0)) → U49(f507_in(z0), s(z0))
U49(f507_out1(z0), s(z1)) → f605_out1(s(z0))
f271_in(s(0)) → f271_out1(0)
f271_in(s(z0)) → U50(f283_in(z0), s(z0))
U50(f283_out1(z0), s(z1)) → f271_out1(z0)
U50(f283_out2(z0), s(z1)) → f271_out1(z0)
f457_in(s(0)) → f457_out1(0)
f457_in(s(z0)) → U51(f468_in(z0), s(z0))
U51(f468_out1(z0), s(z1)) → f457_out1(z0)
U51(f468_out2(z0), s(z1)) → f457_out1(z0)
f291_in(s(0)) → f291_out1(0)
f291_in(s(z0)) → U52(f303_in(z0), s(z0))
U52(f303_out1(z0), s(z1)) → f291_out1(z0)
U52(f303_out2(z0), s(z1)) → f291_out1(z0)
f477_in(s(z0)) → U53(f363_in(z0), s(z0))
U53(f363_out1(z0), s(z1)) → f477_out1(s(z0))
f311_in(s(0)) → f311_out1(0)
f311_in(s(z0)) → U54(f323_in(z0), s(z0))
U54(f323_out1(z0), s(z1)) → f311_out1(z0)
U54(f323_out2(z0), s(z1)) → f311_out1(z0)
f331_in(s(z0)) → U55(f194_in(z0), s(z0))
U55(f194_out1(z0), s(z1)) → f331_out1(s(z0))
f15_in(z0, z1) → U56(f21_in(z0, z1), f22_in(z0, z1), z0, z1)
U56(f21_out1(z0), z1, z2, z3) → f15_out1(z0)
U56(z0, f22_out1(z1), z2, z3) → f15_out2(z1)
f35_in(z0, z1) → U57(f41_in(z0, z1), f42_in(z0, z1), z0, z1)
U57(f41_out1(z0), z1, z2, z3) → f35_out1(z0)
U57(z0, f42_out1(z1), z2, z3) → f35_out2(z1)
f50_in(z0, z1) → U58(f59_in(z0, z1), f60_in(z0, z1), z0, z1)
U58(f59_out1(z0), z1, z2, z3) → f50_out1(z0)
U58(z0, f60_out1(z1), z2, z3) → f50_out2(z1)
f70_in(z0, z1) → U59(f79_in(z0, z1), f80_in(z0, z1), z0, z1)
U59(f79_out1(z0), z1, z2, z3) → f70_out1(z0)
U59(z0, f80_out1(z1), z2, z3) → f70_out2(z1)
f91_in(z0, z1) → U60(f99_in(z0, z1), f100_in(z0, z1), z0, z1)
U60(f99_out1(z0), z1, z2, z3) → f91_out1(z0)
U60(z0, f100_out1(z1), z2, z3) → f91_out2(z1)
f110_in(z0, z1) → U61(f119_in(z0, z1), f120_in(z0, z1), z0, z1)
U61(f119_out1(z0), z1, z2, z3) → f110_out1(z0)
U61(z0, f120_out1(z1), z2, z3) → f110_out2(z1)
f131_in(z0, z1) → U62(f139_in(z0, z1), f140_in(z0, z1), z0, z1)
U62(f139_out1(z0), z1, z2, z3) → f131_out1(z0)
U62(z0, f140_out1(z1), z2, z3) → f131_out2(z1)
f151_in(z0, z1) → U63(f159_in(z0, z1), f161_in(z0, z1), z0, z1)
U63(f159_out1(z0), z1, z2, z3) → f151_out1(z0)
U63(z0, f161_out1(z1), z2, z3) → f151_out2(z1)
f174_in(z0, z1, z2) → U64(f182_in(z0, z1, z2), f184_in(z0, z1, z2), z0, z1, z2)
U64(f182_out1(z0), z1, z2, z3, z4) → f174_out1(z0)
U64(z0, f184_out1(z1), z2, z3, z4) → f174_out2(z1)
f202_in(z0) → U65(f210_in(z0), f212_in(z0), z0)
U65(f210_out1(z0), z1, z2) → f202_out1(z0)
U65(z0, f212_out1(z1), z2) → f202_out2(z1)
f223_in(z0) → U66(f230_in(z0), f232_in(z0), z0)
U66(f230_out1(z0), z1, z2) → f223_out1(z0)
U66(z0, f232_out1(z1), z2) → f223_out2(z1)
f243_in(z0) → U67(f250_in(z0), f252_in(z0), z0)
U67(f250_out1(z0), z1, z2) → f243_out1(z0)
U67(z0, f252_out1(z1), z2) → f243_out2(z1)
f263_in(z0) → U68(f271_in(z0), f272_in(z0), z0)
U68(f271_out1(z0), z1, z2) → f263_out1(z0)
U68(z0, f272_out1(z1), z2) → f263_out2(z1)
f283_in(z0) → U69(f291_in(z0), f292_in(z0), z0)
U69(f291_out1(z0), z1, z2) → f283_out1(z0)
U69(z0, f292_out1(z1), z2) → f283_out2(z1)
f303_in(z0) → U70(f311_in(z0), f312_in(z0), z0)
U70(f311_out1(z0), z1, z2) → f303_out1(z0)
U70(z0, f312_out1(z1), z2) → f303_out2(z1)
f323_in(z0) → U71(f331_in(z0), f332_in(z0), z0)
U71(f331_out1(z0), z1, z2) → f323_out1(z0)
U71(z0, f332_out1(z1), z2) → f323_out2(z1)
f371_in(z0) → U72(f379_in(z0), f380_in(z0), z0)
U72(f379_out1(z0), z1, z2) → f371_out1(z0)
U72(z0, f380_out1(z1), z2) → f371_out2(z1)
f391_in(z0) → U73(f399_in(z0), f400_in(z0), z0)
U73(f399_out1(z0), z1, z2) → f391_out1(z0)
U73(z0, f400_out1(z1), z2) → f391_out2(z1)
f411_in(z0) → U74(f419_in(z0), f420_in(z0), z0)
U74(f419_out1(z0), z1, z2) → f411_out1(z0)
U74(z0, f420_out1(z1), z2) → f411_out2(z1)
f433_in(z0) → U75(f439_in(z0), f440_in(z0), z0)
U75(f439_out1(z0), z1, z2) → f433_out1(z0)
U75(z0, f440_out1(z1), z2) → f433_out2(z1)
f448_in(z0) → U76(f457_in(z0), f458_in(z0), z0)
U76(f457_out1(z0), z1, z2) → f448_out1(z0)
U76(z0, f458_out1(z1), z2) → f448_out2(z1)
f468_in(z0) → U77(f477_in(z0), f478_in(z0), z0)
U77(f477_out1(z0), z1, z2) → f468_out1(z0)
U77(z0, f478_out1(z1), z2) → f468_out2(z1)
f514_in(z0) → U78(f523_in(z0), f524_in(z0), z0)
U78(f523_out1(z0), z1, z2) → f514_out1(z0)
U78(z0, f524_out1(z1), z2) → f514_out2(z1)
f534_in(z0) → U79(f543_in(z0), f544_in(z0), z0)
U79(f543_out1(z0), z1, z2) → f534_out1(z0)
U79(z0, f544_out1(z1), z2) → f534_out2(z1)
f554_in(z0) → U80(f563_in(z0), f564_in(z0), z0)
U80(f563_out1(z0), z1, z2) → f554_out1(z0)
U80(z0, f564_out1(z1), z2) → f554_out2(z1)
f574_in(z0) → U81(f583_in(z0), f584_in(z0), z0)
U81(f583_out1(z0), z1, z2) → f574_out1(z0)
U81(z0, f584_out1(z1), z2) → f574_out2(z1)
f598_in(z0) → U82(f605_in(z0), f606_in(z0), z0)
U82(f605_out1(z0), z1, z2) → f598_out1(z0)
U82(z0, f606_out1(z1), z2) → f598_out2(z1)
f642_in(z0) → U83(f649_in(z0), f650_in(z0), z0)
U83(f649_out1(z0), z1, z2) → f642_out1(z0)
U83(z0, f650_out1(z1), z2) → f642_out2(z1)
f662_in(z0) → U84(f669_in(z0), f670_in(z0), z0)
U84(f669_out1(z0), z1, z2) → f662_out1(z0)
U84(z0, f670_out1(z1), z2) → f662_out2(z1)
f682_in(z0) → U85(f689_in(z0), f690_in(z0), z0)
U85(f689_out1(z0), z1, z2) → f682_out1(z0)
U85(z0, f690_out1(z1), z2) → f682_out2(z1)
f703_in(z0) → U86(f709_in(z0), f710_in(z0), z0)
U86(f709_out1(z0), z1, z2) → f703_out1(z0)
U86(z0, f710_out1(z1), z2) → f703_out2(z1)
f745_in(z0) → U87(f751_in(z0), f752_in(z0), z0)
U87(f751_out1(z0), z1, z2) → f745_out1(z0)
U87(z0, f752_out1(z1), z2) → f745_out2(z1)
f765_in(z0) → U88(f771_in(z0), f772_in(z0), z0)
U88(f771_out1(z0), z1, z2) → f765_out1(z0)
U88(z0, f772_out1(z1), z2) → f765_out2(z1)
f787_in(z0) → U89(f793_in(z0), f794_in(z0), z0)
U89(f793_out1(z0), z1, z2) → f787_out1(z0)
U89(z0, f794_out1(z1), z2) → f787_out2(z1)
f824_in(z0) → U90(f829_in(z0), f830_in(z0), z0)
U90(f829_out1(z0), z1, z2) → f824_out1(z0)
U90(z0, f830_out1(z1), z2) → f824_out2(z1)
f837_in(z0) → U91(f841_in(z0), f842_in(z0), z0)
U91(f841_out1(z0), z1, z2) → f837_out1(z0)
U91(z0, f842_out1(z1), z2) → f837_out2(z1)
f866_in(z0) → U92(f870_in(z0), f871_in(z0), z0)
U92(f870_out1(z0), z1, z2) → f866_out1(z0)
U92(z0, f871_out1(z1), z2) → f866_out2(z1)
Tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F21_IN(s(z0), s(0)) → c39(F35_IN(z0, 0))
F21_IN(s(s(y0)), s(s(y1))) → c39(F35_IN(s(y0), s(y1)))
F50_IN(z0, 0) → c2(F60_IN(z0, 0))
F50_IN(s(y0), s(y1)) → c190(F59_IN(s(y0), s(y1)))
F50_IN(z0, 0) → c2
S tuples:

F42_IN(z0, 0) → c1(F860_IN(z0))
F60_IN(z0, 0) → c1(F816_IN(z0))
F80_IN(z0, 0) → c1(F736_IN(z0))
F100_IN(z0, 0) → c1(F633_IN(z0))
F120_IN(z0, 0) → c1(F507_IN(z0))
F140_IN(z0, 0) → c1(F363_IN(z0))
F161_IN(z0, 0) → c1(F194_IN(z0))
F860_IN(z0) → c3(F866_IN(z0))
F816_IN(z0) → c7(F824_IN(z0))
F167_IN(z0, z1, z2) → c11(F174_IN(z0, z1, z2))
F736_IN(z0) → c15(F745_IN(z0))
F633_IN(z0) → c23(F642_IN(z0))
F507_IN(z0) → c27(F514_IN(z0))
F363_IN(z0) → c31(F371_IN(z0))
F194_IN(z0) → c35(F202_IN(z0))
F41_IN(s(z0), s(z1)) → c43(F50_IN(z0, z1))
F59_IN(s(z0), s(z1)) → c49(F70_IN(z0, z1))
F870_IN(s(z0)) → c54(F860_IN(z0))
F79_IN(s(z0), s(z1)) → c57(F91_IN(z0, z1))
F829_IN(s(z0)) → c63(F837_IN(z0))
F99_IN(s(z0), s(z1)) → c67(F110_IN(z0, z1))
F751_IN(s(z0)) → c73(F765_IN(z0))
F841_IN(s(z0)) → c76(F816_IN(z0))
F119_IN(s(z0), s(z1)) → c79(F131_IN(z0, z1))
F649_IN(s(z0)) → c85(F662_IN(z0))
F771_IN(s(z0)) → c89(F787_IN(z0))
F139_IN(s(z0), s(z1)) → c93(F151_IN(z0, z1))
F523_IN(s(z0)) → c99(F534_IN(z0))
F669_IN(s(z0)) → c103(F682_IN(z0))
F793_IN(s(z0)) → c106(F736_IN(z0))
F159_IN(s(z0), s(z1)) → c108(F167_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F379_IN(s(z0)) → c113(F391_IN(z0))
F543_IN(s(z0)) → c117(F554_IN(z0))
F689_IN(s(z0)) → c121(F703_IN(z0))
F210_IN(s(z0)) → c125(F223_IN(z0))
F399_IN(s(z0)) → c129(F411_IN(z0))
F563_IN(s(z0)) → c133(F574_IN(z0))
F709_IN(s(z0)) → c136(F633_IN(z0))
F182_IN(s(z0), s(z1), z2) → c138(F167_IN(z0, z1, z2))
F184_IN(z0, 0, z1) → c140(F7_IN(z0, s(z1)))
F230_IN(s(z0)) → c143(F243_IN(z0))
F419_IN(s(z0)) → c147(F433_IN(z0))
F583_IN(s(z0)) → c151(F598_IN(z0))
F250_IN(s(z0)) → c155(F263_IN(z0))
F439_IN(s(z0)) → c159(F448_IN(z0))
F605_IN(s(z0)) → c162(F507_IN(z0))
F271_IN(s(z0)) → c165(F283_IN(z0))
F457_IN(s(z0)) → c169(F468_IN(z0))
F291_IN(s(z0)) → c173(F303_IN(z0))
F477_IN(s(z0)) → c176(F363_IN(z0))
F311_IN(s(z0)) → c179(F323_IN(z0))
F331_IN(s(z0)) → c182(F194_IN(z0))
F70_IN(z0, z1) → c193(F79_IN(z0, z1), F80_IN(z0, z1))
F91_IN(z0, z1) → c196(F99_IN(z0, z1), F100_IN(z0, z1))
F110_IN(z0, z1) → c199(F119_IN(z0, z1), F120_IN(z0, z1))
F131_IN(z0, z1) → c202(F139_IN(z0, z1), F140_IN(z0, z1))
F151_IN(z0, z1) → c205(F159_IN(z0, z1), F161_IN(z0, z1))
F174_IN(z0, z1, z2) → c208(F182_IN(z0, z1, z2), F184_IN(z0, z1, z2))
F202_IN(z0) → c211(F210_IN(z0))
F223_IN(z0) → c214(F230_IN(z0))
F243_IN(z0) → c217(F250_IN(z0))
F263_IN(z0) → c220(F271_IN(z0))
F283_IN(z0) → c223(F291_IN(z0))
F303_IN(z0) → c226(F311_IN(z0))
F323_IN(z0) → c229(F331_IN(z0))
F371_IN(z0) → c232(F379_IN(z0))
F391_IN(z0) → c235(F399_IN(z0))
F411_IN(z0) → c238(F419_IN(z0))
F433_IN(z0) → c241(F439_IN(z0))
F448_IN(z0) → c244(F457_IN(z0))
F468_IN(z0) → c247(F477_IN(z0))
F514_IN(z0) → c250(F523_IN(z0))
F534_IN(z0) → c253(F543_IN(z0))
F554_IN(z0) → c256(F563_IN(z0))
F574_IN(z0) → c259(F583_IN(z0))
F598_IN(z0) → c262(F605_IN(z0))
F642_IN(z0) → c265(F649_IN(z0))
F662_IN(z0) → c268(F669_IN(z0))
F682_IN(z0) → c271(F689_IN(z0))
F703_IN(z0) → c274(F709_IN(z0))
F745_IN(z0) → c277(F751_IN(z0))
F765_IN(z0) → c280(F771_IN(z0))
F787_IN(z0) → c283(F793_IN(z0))
F824_IN(z0) → c286(F829_IN(z0))
F837_IN(z0) → c289(F841_IN(z0))
F866_IN(z0) → c292(F870_IN(z0))
F15_IN(s(y0), s(y1)) → c184(F21_IN(s(y0), s(y1)))
F7_IN(x0, s(x1)) → c19(F15_IN(x0, s(x1)))
F35_IN(z0, 0) → c(F42_IN(z0, 0))
F35_IN(s(y0), s(y1)) → c187(F41_IN(s(y0), s(y1)))
F21_IN(s(z0), s(0)) → c39(F35_IN(z0, 0))
F21_IN(s(s(y0)), s(s(y1))) → c39(F35_IN(s(y0), s(y1)))
F50_IN(z0, 0) → c2(F60_IN(z0, 0))
F50_IN(s(y0), s(y1)) → c190(F59_IN(s(y0), s(y1)))
F50_IN(z0, 0) → c2
K tuples:none
Defined Rule Symbols:

f1_in, U1, f860_in, U2, f816_in, U3, f167_in, U4, f736_in, U5, f7_in, U6, f633_in, U7, f507_in, U8, f363_in, U9, f194_in, U10, f21_in, U11, f41_in, U12, f42_in, U13, f59_in, U14, f60_in, U15, f870_in, U16, f79_in, U17, f80_in, U18, f829_in, U19, f99_in, U20, f100_in, U21, f751_in, U22, f841_in, U23, f119_in, U24, f120_in, U25, f649_in, U26, f771_in, U27, f139_in, U28, f140_in, U29, f523_in, U30, f669_in, U31, f793_in, U32, f159_in, U33, f161_in, U34, f379_in, U35, f543_in, U36, f689_in, U37, f210_in, U38, f399_in, U39, f563_in, U40, f709_in, U41, f182_in, U42, f184_in, U43, f230_in, U44, f419_in, U45, f583_in, U46, f250_in, U47, f439_in, U48, f605_in, U49, f271_in, U50, f457_in, U51, f291_in, U52, f477_in, U53, f311_in, U54, f331_in, U55, f15_in, U56, f35_in, U57, f50_in, U58, f70_in, U59, f91_in, U60, f110_in, U61, f131_in, U62, f151_in, U63, f174_in, U64, f202_in, U65, f223_in, U66, f243_in, U67, f263_in, U68, f283_in, U69, f303_in, U70, f323_in, U71, f371_in, U72, f391_in, U73, f411_in, U74, f433_in, U75, f448_in, U76, f468_in, U77, f514_in, U78, f534_in, U79, f554_in, U80, f574_in, U81, f598_in, U82, f642_in, U83, f662_in, U84, f682_in, U85, f703_in, U86, f745_in, U87, f765_in, U88, f787_in, U89, f824_in, U90, f837_in, U91, f866_in, U92

Defined Pair Symbols:

F42_IN, F60_IN, F80_IN, F100_IN, F120_IN, F140_IN, F161_IN, F860_IN, F816_IN, F167_IN, F736_IN, F633_IN, F507_IN, F363_IN, F194_IN, F41_IN, F59_IN, F870_IN, F79_IN, F829_IN, F99_IN, F751_IN, F841_IN, F119_IN, F649_IN, F771_IN, F139_IN, F523_IN, F669_IN, F793_IN, F159_IN, F379_IN, F543_IN, F689_IN, F210_IN, F399_IN, F563_IN, F709_IN, F182_IN, F184_IN, F230_IN, F419_IN, F583_IN, F250_IN, F439_IN, F605_IN, F271_IN, F457_IN, F291_IN, F477_IN, F311_IN, F331_IN, F70_IN, F91_IN, F110_IN, F131_IN, F151_IN, F174_IN, F202_IN, F223_IN, F243_IN, F263_IN, F283_IN, F303_IN, F323_IN, F371_IN, F391_IN, F411_IN, F433_IN, F448_IN, F468_IN, F514_IN, F534_IN, F554_IN, F574_IN, F598_IN, F642_IN, F662_IN, F682_IN, F703_IN, F745_IN, F765_IN, F787_IN, F824_IN, F837_IN, F866_IN, F15_IN, F7_IN, F35_IN, F21_IN, F50_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c, c187, c39, c2, c190, c2

(35) PrologToCdtProblemTransformerProof (UPPER BOUND (ID) transformation)

Built complexity over-approximating cdt problems from derivation graph.

(36) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F2_IN(z0, z1) → c(U1'(f5_in(z0, z1), z0, z1), F5_IN(z0, z1))
F889_IN(z0) → c3(U2'(f894_in(z0), z0), F894_IN(z0))
F812_IN(z0) → c7(U3'(f819_in(z0), z0), F819_IN(z0))
F168_IN(z0, z1, z2) → c11(U4'(f173_in(z0, z1, z2), z0, z1, z2), F173_IN(z0, z1, z2))
F733_IN(z0) → c15(U5'(f739_in(z0), z0), F739_IN(z0))
F5_IN(z0, z1) → c19(U6'(f9_in(z0, z1), z0, z1), F9_IN(z0, z1))
F631_IN(z0) → c23(U7'(f638_in(z0), z0), F638_IN(z0))
F509_IN(z0) → c27(U8'(f517_in(z0), z0), F517_IN(z0))
F361_IN(z0) → c31(U9'(f368_in(z0), z0), F368_IN(z0))
F193_IN(z0) → c35(U10'(f201_in(z0), z0), F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(U11'(f30_in(z0, z1), s(z0), s(z1)), F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(U12'(f55_in(z0, z1), s(z0), s(z1)), F55_IN(z0, z1))
F40_IN(z0, 0) → c46(U13'(f889_in(z0), z0, 0), F889_IN(z0))
F61_IN(s(z0), s(z1)) → c49(U14'(f74_in(z0, z1), s(z0), s(z1)), F74_IN(z0, z1))
F62_IN(z0, 0) → c52(U15'(f812_in(z0), z0, 0), F812_IN(z0))
F898_IN(s(z0)) → c54(U16'(f889_in(z0), s(z0)), F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(U17'(f94_in(z0, z1), s(z0), s(z1)), F94_IN(z0, z1))
F82_IN(z0, 0) → c60(U18'(f733_in(z0), z0, 0), F733_IN(z0))
F833_IN(s(z0)) → c63(U19'(f852_in(z0), s(z0)), F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(U20'(f113_in(z0, z1), s(z0), s(z1)), F113_IN(z0, z1))
F102_IN(z0, 0) → c70(U21'(f631_in(z0), z0, 0), F631_IN(z0))
F748_IN(s(z0)) → c73(U22'(f759_in(z0), s(z0)), F759_IN(z0))
F863_IN(s(z0)) → c76(U23'(f812_in(z0), s(z0)), F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(U24'(f133_in(z0, z1), s(z0), s(z1)), F133_IN(z0, z1))
F122_IN(z0, 0) → c82(U25'(f509_in(z0), z0, 0), F509_IN(z0))
F647_IN(s(z0)) → c85(U26'(f658_in(z0), s(z0)), F658_IN(z0))
F767_IN(s(z0)) → c89(U27'(f777_in(z0), s(z0)), F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(U28'(f153_in(z0, z1), s(z0), s(z1)), F153_IN(z0, z1))
F142_IN(z0, 0) → c96(U29'(f361_in(z0), z0, 0), F361_IN(z0))
F525_IN(s(z0)) → c99(U30'(f537_in(z0), s(z0)), F537_IN(z0))
F667_IN(s(z0)) → c103(U31'(f678_in(z0), s(z0)), F678_IN(z0))
F784_IN(s(z0)) → c106(U32'(f733_in(z0), s(z0)), F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(U33'(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1)), F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F162_IN(z0, 0) → c110(U34'(f193_in(z0), z0, 0), F193_IN(z0))
F377_IN(s(z0)) → c113(U35'(f388_in(z0), s(z0)), F388_IN(z0))
F545_IN(s(z0)) → c117(U36'(f557_in(z0), s(z0)), F557_IN(z0))
F687_IN(s(z0)) → c121(U37'(f697_in(z0), s(z0)), F697_IN(z0))
F209_IN(s(z0)) → c125(U38'(f221_in(z0), s(z0)), F221_IN(z0))
F397_IN(s(z0)) → c129(U39'(f408_in(z0), s(z0)), F408_IN(z0))
F565_IN(s(z0)) → c133(U40'(f577_in(z0), s(z0)), F577_IN(z0))
F707_IN(s(z0)) → c136(U41'(f631_in(z0), s(z0)), F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(U42'(f168_in(z0, z1, z2), s(z0), s(z1), z2), F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(U43'(f5_in(z0, s(z1)), z0, 0, z1), F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(U44'(f241_in(z0), s(z0)), F241_IN(z0))
F417_IN(s(z0)) → c147(U45'(f428_in(z0), s(z0)), F428_IN(z0))
F585_IN(s(z0)) → c151(U46'(f594_in(z0), s(z0)), F594_IN(z0))
F249_IN(s(z0)) → c155(U47'(f261_in(z0), s(z0)), F261_IN(z0))
F437_IN(s(z0)) → c159(U48'(f453_in(z0), s(z0)), F453_IN(z0))
F603_IN(s(z0)) → c162(U49'(f509_in(z0), s(z0)), F509_IN(z0))
F269_IN(s(z0)) → c165(U50'(f280_in(z0), s(z0)), F280_IN(z0))
F459_IN(s(z0)) → c169(U51'(f472_in(z0), s(z0)), F472_IN(z0))
F289_IN(s(z0)) → c173(U52'(f300_in(z0), s(z0)), F300_IN(z0))
F479_IN(s(z0)) → c176(U53'(f361_in(z0), s(z0)), F361_IN(z0))
F309_IN(s(z0)) → c179(U54'(f320_in(z0), s(z0)), F320_IN(z0))
F329_IN(s(z0)) → c182(U55'(f193_in(z0), s(z0)), F193_IN(z0))
F9_IN(z0, z1) → c184(U56'(f18_in(z0, z1), f20_in(z0, z1), z0, z1), F18_IN(z0, z1))
F30_IN(z0, z1) → c187(U57'(f39_in(z0, z1), f40_in(z0, z1), z0, z1), F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(U58'(f61_in(z0, z1), f62_in(z0, z1), z0, z1), F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(U59'(f81_in(z0, z1), f82_in(z0, z1), z0, z1), F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(U60'(f101_in(z0, z1), f102_in(z0, z1), z0, z1), F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(U61'(f121_in(z0, z1), f122_in(z0, z1), z0, z1), F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(U62'(f141_in(z0, z1), f142_in(z0, z1), z0, z1), F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(U63'(f160_in(z0, z1), f162_in(z0, z1), z0, z1), F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(U64'(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2), F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(U65'(f209_in(z0), f211_in(z0), z0), F209_IN(z0))
F221_IN(z0) → c214(U66'(f229_in(z0), f231_in(z0), z0), F229_IN(z0))
F241_IN(z0) → c217(U67'(f249_in(z0), f251_in(z0), z0), F249_IN(z0))
F261_IN(z0) → c220(U68'(f269_in(z0), f270_in(z0), z0), F269_IN(z0))
F280_IN(z0) → c223(U69'(f289_in(z0), f290_in(z0), z0), F289_IN(z0))
F300_IN(z0) → c226(U70'(f309_in(z0), f310_in(z0), z0), F309_IN(z0))
F320_IN(z0) → c229(U71'(f329_in(z0), f330_in(z0), z0), F329_IN(z0))
F368_IN(z0) → c232(U72'(f377_in(z0), f378_in(z0), z0), F377_IN(z0))
F388_IN(z0) → c235(U73'(f397_in(z0), f398_in(z0), z0), F397_IN(z0))
F408_IN(z0) → c238(U74'(f417_in(z0), f418_in(z0), z0), F417_IN(z0))
F428_IN(z0) → c241(U75'(f437_in(z0), f438_in(z0), z0), F437_IN(z0))
F453_IN(z0) → c244(U76'(f459_in(z0), f460_in(z0), z0), F459_IN(z0))
F472_IN(z0) → c247(U77'(f479_in(z0), f480_in(z0), z0), F479_IN(z0))
F517_IN(z0) → c250(U78'(f525_in(z0), f526_in(z0), z0), F525_IN(z0))
F537_IN(z0) → c253(U79'(f545_in(z0), f546_in(z0), z0), F545_IN(z0))
F557_IN(z0) → c256(U80'(f565_in(z0), f566_in(z0), z0), F565_IN(z0))
F577_IN(z0) → c259(U81'(f585_in(z0), f586_in(z0), z0), F585_IN(z0))
F594_IN(z0) → c262(U82'(f603_in(z0), f604_in(z0), z0), F603_IN(z0))
F638_IN(z0) → c265(U83'(f647_in(z0), f648_in(z0), z0), F647_IN(z0))
F658_IN(z0) → c268(U84'(f667_in(z0), f668_in(z0), z0), F667_IN(z0))
F678_IN(z0) → c271(U85'(f687_in(z0), f688_in(z0), z0), F687_IN(z0))
F697_IN(z0) → c274(U86'(f707_in(z0), f708_in(z0), z0), F707_IN(z0))
F739_IN(z0) → c277(U87'(f748_in(z0), f749_in(z0), z0), F748_IN(z0))
F759_IN(z0) → c280(U88'(f767_in(z0), f768_in(z0), z0), F767_IN(z0))
F777_IN(z0) → c283(U89'(f784_in(z0), f785_in(z0), z0), F784_IN(z0))
F819_IN(z0) → c286(U90'(f833_in(z0), f834_in(z0), z0), F833_IN(z0))
F852_IN(z0) → c289(U91'(f863_in(z0), f864_in(z0), z0), F863_IN(z0))
F894_IN(z0) → c292(U92'(f898_in(z0), f899_in(z0), z0), F898_IN(z0))
S tuples:

F2_IN(z0, z1) → c(U1'(f5_in(z0, z1), z0, z1), F5_IN(z0, z1))
F889_IN(z0) → c3(U2'(f894_in(z0), z0), F894_IN(z0))
F812_IN(z0) → c7(U3'(f819_in(z0), z0), F819_IN(z0))
F168_IN(z0, z1, z2) → c11(U4'(f173_in(z0, z1, z2), z0, z1, z2), F173_IN(z0, z1, z2))
F733_IN(z0) → c15(U5'(f739_in(z0), z0), F739_IN(z0))
F5_IN(z0, z1) → c19(U6'(f9_in(z0, z1), z0, z1), F9_IN(z0, z1))
F631_IN(z0) → c23(U7'(f638_in(z0), z0), F638_IN(z0))
F509_IN(z0) → c27(U8'(f517_in(z0), z0), F517_IN(z0))
F361_IN(z0) → c31(U9'(f368_in(z0), z0), F368_IN(z0))
F193_IN(z0) → c35(U10'(f201_in(z0), z0), F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(U11'(f30_in(z0, z1), s(z0), s(z1)), F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(U12'(f55_in(z0, z1), s(z0), s(z1)), F55_IN(z0, z1))
F40_IN(z0, 0) → c46(U13'(f889_in(z0), z0, 0), F889_IN(z0))
F61_IN(s(z0), s(z1)) → c49(U14'(f74_in(z0, z1), s(z0), s(z1)), F74_IN(z0, z1))
F62_IN(z0, 0) → c52(U15'(f812_in(z0), z0, 0), F812_IN(z0))
F898_IN(s(z0)) → c54(U16'(f889_in(z0), s(z0)), F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(U17'(f94_in(z0, z1), s(z0), s(z1)), F94_IN(z0, z1))
F82_IN(z0, 0) → c60(U18'(f733_in(z0), z0, 0), F733_IN(z0))
F833_IN(s(z0)) → c63(U19'(f852_in(z0), s(z0)), F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(U20'(f113_in(z0, z1), s(z0), s(z1)), F113_IN(z0, z1))
F102_IN(z0, 0) → c70(U21'(f631_in(z0), z0, 0), F631_IN(z0))
F748_IN(s(z0)) → c73(U22'(f759_in(z0), s(z0)), F759_IN(z0))
F863_IN(s(z0)) → c76(U23'(f812_in(z0), s(z0)), F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(U24'(f133_in(z0, z1), s(z0), s(z1)), F133_IN(z0, z1))
F122_IN(z0, 0) → c82(U25'(f509_in(z0), z0, 0), F509_IN(z0))
F647_IN(s(z0)) → c85(U26'(f658_in(z0), s(z0)), F658_IN(z0))
F767_IN(s(z0)) → c89(U27'(f777_in(z0), s(z0)), F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(U28'(f153_in(z0, z1), s(z0), s(z1)), F153_IN(z0, z1))
F142_IN(z0, 0) → c96(U29'(f361_in(z0), z0, 0), F361_IN(z0))
F525_IN(s(z0)) → c99(U30'(f537_in(z0), s(z0)), F537_IN(z0))
F667_IN(s(z0)) → c103(U31'(f678_in(z0), s(z0)), F678_IN(z0))
F784_IN(s(z0)) → c106(U32'(f733_in(z0), s(z0)), F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(U33'(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1)), F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F162_IN(z0, 0) → c110(U34'(f193_in(z0), z0, 0), F193_IN(z0))
F377_IN(s(z0)) → c113(U35'(f388_in(z0), s(z0)), F388_IN(z0))
F545_IN(s(z0)) → c117(U36'(f557_in(z0), s(z0)), F557_IN(z0))
F687_IN(s(z0)) → c121(U37'(f697_in(z0), s(z0)), F697_IN(z0))
F209_IN(s(z0)) → c125(U38'(f221_in(z0), s(z0)), F221_IN(z0))
F397_IN(s(z0)) → c129(U39'(f408_in(z0), s(z0)), F408_IN(z0))
F565_IN(s(z0)) → c133(U40'(f577_in(z0), s(z0)), F577_IN(z0))
F707_IN(s(z0)) → c136(U41'(f631_in(z0), s(z0)), F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(U42'(f168_in(z0, z1, z2), s(z0), s(z1), z2), F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(U43'(f5_in(z0, s(z1)), z0, 0, z1), F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(U44'(f241_in(z0), s(z0)), F241_IN(z0))
F417_IN(s(z0)) → c147(U45'(f428_in(z0), s(z0)), F428_IN(z0))
F585_IN(s(z0)) → c151(U46'(f594_in(z0), s(z0)), F594_IN(z0))
F249_IN(s(z0)) → c155(U47'(f261_in(z0), s(z0)), F261_IN(z0))
F437_IN(s(z0)) → c159(U48'(f453_in(z0), s(z0)), F453_IN(z0))
F603_IN(s(z0)) → c162(U49'(f509_in(z0), s(z0)), F509_IN(z0))
F269_IN(s(z0)) → c165(U50'(f280_in(z0), s(z0)), F280_IN(z0))
F459_IN(s(z0)) → c169(U51'(f472_in(z0), s(z0)), F472_IN(z0))
F289_IN(s(z0)) → c173(U52'(f300_in(z0), s(z0)), F300_IN(z0))
F479_IN(s(z0)) → c176(U53'(f361_in(z0), s(z0)), F361_IN(z0))
F309_IN(s(z0)) → c179(U54'(f320_in(z0), s(z0)), F320_IN(z0))
F329_IN(s(z0)) → c182(U55'(f193_in(z0), s(z0)), F193_IN(z0))
F9_IN(z0, z1) → c184(U56'(f18_in(z0, z1), f20_in(z0, z1), z0, z1), F18_IN(z0, z1))
F30_IN(z0, z1) → c187(U57'(f39_in(z0, z1), f40_in(z0, z1), z0, z1), F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(U58'(f61_in(z0, z1), f62_in(z0, z1), z0, z1), F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(U59'(f81_in(z0, z1), f82_in(z0, z1), z0, z1), F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(U60'(f101_in(z0, z1), f102_in(z0, z1), z0, z1), F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(U61'(f121_in(z0, z1), f122_in(z0, z1), z0, z1), F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(U62'(f141_in(z0, z1), f142_in(z0, z1), z0, z1), F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(U63'(f160_in(z0, z1), f162_in(z0, z1), z0, z1), F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(U64'(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2), F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(U65'(f209_in(z0), f211_in(z0), z0), F209_IN(z0))
F221_IN(z0) → c214(U66'(f229_in(z0), f231_in(z0), z0), F229_IN(z0))
F241_IN(z0) → c217(U67'(f249_in(z0), f251_in(z0), z0), F249_IN(z0))
F261_IN(z0) → c220(U68'(f269_in(z0), f270_in(z0), z0), F269_IN(z0))
F280_IN(z0) → c223(U69'(f289_in(z0), f290_in(z0), z0), F289_IN(z0))
F300_IN(z0) → c226(U70'(f309_in(z0), f310_in(z0), z0), F309_IN(z0))
F320_IN(z0) → c229(U71'(f329_in(z0), f330_in(z0), z0), F329_IN(z0))
F368_IN(z0) → c232(U72'(f377_in(z0), f378_in(z0), z0), F377_IN(z0))
F388_IN(z0) → c235(U73'(f397_in(z0), f398_in(z0), z0), F397_IN(z0))
F408_IN(z0) → c238(U74'(f417_in(z0), f418_in(z0), z0), F417_IN(z0))
F428_IN(z0) → c241(U75'(f437_in(z0), f438_in(z0), z0), F437_IN(z0))
F453_IN(z0) → c244(U76'(f459_in(z0), f460_in(z0), z0), F459_IN(z0))
F472_IN(z0) → c247(U77'(f479_in(z0), f480_in(z0), z0), F479_IN(z0))
F517_IN(z0) → c250(U78'(f525_in(z0), f526_in(z0), z0), F525_IN(z0))
F537_IN(z0) → c253(U79'(f545_in(z0), f546_in(z0), z0), F545_IN(z0))
F557_IN(z0) → c256(U80'(f565_in(z0), f566_in(z0), z0), F565_IN(z0))
F577_IN(z0) → c259(U81'(f585_in(z0), f586_in(z0), z0), F585_IN(z0))
F594_IN(z0) → c262(U82'(f603_in(z0), f604_in(z0), z0), F603_IN(z0))
F638_IN(z0) → c265(U83'(f647_in(z0), f648_in(z0), z0), F647_IN(z0))
F658_IN(z0) → c268(U84'(f667_in(z0), f668_in(z0), z0), F667_IN(z0))
F678_IN(z0) → c271(U85'(f687_in(z0), f688_in(z0), z0), F687_IN(z0))
F697_IN(z0) → c274(U86'(f707_in(z0), f708_in(z0), z0), F707_IN(z0))
F739_IN(z0) → c277(U87'(f748_in(z0), f749_in(z0), z0), F748_IN(z0))
F759_IN(z0) → c280(U88'(f767_in(z0), f768_in(z0), z0), F767_IN(z0))
F777_IN(z0) → c283(U89'(f784_in(z0), f785_in(z0), z0), F784_IN(z0))
F819_IN(z0) → c286(U90'(f833_in(z0), f834_in(z0), z0), F833_IN(z0))
F852_IN(z0) → c289(U91'(f863_in(z0), f864_in(z0), z0), F863_IN(z0))
F894_IN(z0) → c292(U92'(f898_in(z0), f899_in(z0), z0), F898_IN(z0))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F2_IN, F889_IN, F812_IN, F168_IN, F733_IN, F5_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F40_IN, F61_IN, F62_IN, F898_IN, F81_IN, F82_IN, F833_IN, F101_IN, F102_IN, F748_IN, F863_IN, F121_IN, F122_IN, F647_IN, F767_IN, F141_IN, F142_IN, F525_IN, F667_IN, F784_IN, F160_IN, F162_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F183_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F9_IN, F30_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN

Compound Symbols:

c, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c46, c49, c52, c54, c57, c60, c63, c67, c70, c73, c76, c79, c82, c85, c89, c93, c96, c99, c103, c106, c108, c110, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c184, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292

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

Split RHS of tuples not part of any SCC

(38) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F889_IN(z0) → c3(U2'(f894_in(z0), z0), F894_IN(z0))
F812_IN(z0) → c7(U3'(f819_in(z0), z0), F819_IN(z0))
F168_IN(z0, z1, z2) → c11(U4'(f173_in(z0, z1, z2), z0, z1, z2), F173_IN(z0, z1, z2))
F733_IN(z0) → c15(U5'(f739_in(z0), z0), F739_IN(z0))
F5_IN(z0, z1) → c19(U6'(f9_in(z0, z1), z0, z1), F9_IN(z0, z1))
F631_IN(z0) → c23(U7'(f638_in(z0), z0), F638_IN(z0))
F509_IN(z0) → c27(U8'(f517_in(z0), z0), F517_IN(z0))
F361_IN(z0) → c31(U9'(f368_in(z0), z0), F368_IN(z0))
F193_IN(z0) → c35(U10'(f201_in(z0), z0), F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(U11'(f30_in(z0, z1), s(z0), s(z1)), F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(U12'(f55_in(z0, z1), s(z0), s(z1)), F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(U14'(f74_in(z0, z1), s(z0), s(z1)), F74_IN(z0, z1))
F898_IN(s(z0)) → c54(U16'(f889_in(z0), s(z0)), F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(U17'(f94_in(z0, z1), s(z0), s(z1)), F94_IN(z0, z1))
F833_IN(s(z0)) → c63(U19'(f852_in(z0), s(z0)), F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(U20'(f113_in(z0, z1), s(z0), s(z1)), F113_IN(z0, z1))
F748_IN(s(z0)) → c73(U22'(f759_in(z0), s(z0)), F759_IN(z0))
F863_IN(s(z0)) → c76(U23'(f812_in(z0), s(z0)), F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(U24'(f133_in(z0, z1), s(z0), s(z1)), F133_IN(z0, z1))
F647_IN(s(z0)) → c85(U26'(f658_in(z0), s(z0)), F658_IN(z0))
F767_IN(s(z0)) → c89(U27'(f777_in(z0), s(z0)), F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(U28'(f153_in(z0, z1), s(z0), s(z1)), F153_IN(z0, z1))
F525_IN(s(z0)) → c99(U30'(f537_in(z0), s(z0)), F537_IN(z0))
F667_IN(s(z0)) → c103(U31'(f678_in(z0), s(z0)), F678_IN(z0))
F784_IN(s(z0)) → c106(U32'(f733_in(z0), s(z0)), F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(U33'(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1)), F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(U35'(f388_in(z0), s(z0)), F388_IN(z0))
F545_IN(s(z0)) → c117(U36'(f557_in(z0), s(z0)), F557_IN(z0))
F687_IN(s(z0)) → c121(U37'(f697_in(z0), s(z0)), F697_IN(z0))
F209_IN(s(z0)) → c125(U38'(f221_in(z0), s(z0)), F221_IN(z0))
F397_IN(s(z0)) → c129(U39'(f408_in(z0), s(z0)), F408_IN(z0))
F565_IN(s(z0)) → c133(U40'(f577_in(z0), s(z0)), F577_IN(z0))
F707_IN(s(z0)) → c136(U41'(f631_in(z0), s(z0)), F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(U42'(f168_in(z0, z1, z2), s(z0), s(z1), z2), F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(U43'(f5_in(z0, s(z1)), z0, 0, z1), F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(U44'(f241_in(z0), s(z0)), F241_IN(z0))
F417_IN(s(z0)) → c147(U45'(f428_in(z0), s(z0)), F428_IN(z0))
F585_IN(s(z0)) → c151(U46'(f594_in(z0), s(z0)), F594_IN(z0))
F249_IN(s(z0)) → c155(U47'(f261_in(z0), s(z0)), F261_IN(z0))
F437_IN(s(z0)) → c159(U48'(f453_in(z0), s(z0)), F453_IN(z0))
F603_IN(s(z0)) → c162(U49'(f509_in(z0), s(z0)), F509_IN(z0))
F269_IN(s(z0)) → c165(U50'(f280_in(z0), s(z0)), F280_IN(z0))
F459_IN(s(z0)) → c169(U51'(f472_in(z0), s(z0)), F472_IN(z0))
F289_IN(s(z0)) → c173(U52'(f300_in(z0), s(z0)), F300_IN(z0))
F479_IN(s(z0)) → c176(U53'(f361_in(z0), s(z0)), F361_IN(z0))
F309_IN(s(z0)) → c179(U54'(f320_in(z0), s(z0)), F320_IN(z0))
F329_IN(s(z0)) → c182(U55'(f193_in(z0), s(z0)), F193_IN(z0))
F9_IN(z0, z1) → c184(U56'(f18_in(z0, z1), f20_in(z0, z1), z0, z1), F18_IN(z0, z1))
F30_IN(z0, z1) → c187(U57'(f39_in(z0, z1), f40_in(z0, z1), z0, z1), F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(U58'(f61_in(z0, z1), f62_in(z0, z1), z0, z1), F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(U59'(f81_in(z0, z1), f82_in(z0, z1), z0, z1), F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(U60'(f101_in(z0, z1), f102_in(z0, z1), z0, z1), F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(U61'(f121_in(z0, z1), f122_in(z0, z1), z0, z1), F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(U62'(f141_in(z0, z1), f142_in(z0, z1), z0, z1), F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(U63'(f160_in(z0, z1), f162_in(z0, z1), z0, z1), F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(U64'(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2), F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(U65'(f209_in(z0), f211_in(z0), z0), F209_IN(z0))
F221_IN(z0) → c214(U66'(f229_in(z0), f231_in(z0), z0), F229_IN(z0))
F241_IN(z0) → c217(U67'(f249_in(z0), f251_in(z0), z0), F249_IN(z0))
F261_IN(z0) → c220(U68'(f269_in(z0), f270_in(z0), z0), F269_IN(z0))
F280_IN(z0) → c223(U69'(f289_in(z0), f290_in(z0), z0), F289_IN(z0))
F300_IN(z0) → c226(U70'(f309_in(z0), f310_in(z0), z0), F309_IN(z0))
F320_IN(z0) → c229(U71'(f329_in(z0), f330_in(z0), z0), F329_IN(z0))
F368_IN(z0) → c232(U72'(f377_in(z0), f378_in(z0), z0), F377_IN(z0))
F388_IN(z0) → c235(U73'(f397_in(z0), f398_in(z0), z0), F397_IN(z0))
F408_IN(z0) → c238(U74'(f417_in(z0), f418_in(z0), z0), F417_IN(z0))
F428_IN(z0) → c241(U75'(f437_in(z0), f438_in(z0), z0), F437_IN(z0))
F453_IN(z0) → c244(U76'(f459_in(z0), f460_in(z0), z0), F459_IN(z0))
F472_IN(z0) → c247(U77'(f479_in(z0), f480_in(z0), z0), F479_IN(z0))
F517_IN(z0) → c250(U78'(f525_in(z0), f526_in(z0), z0), F525_IN(z0))
F537_IN(z0) → c253(U79'(f545_in(z0), f546_in(z0), z0), F545_IN(z0))
F557_IN(z0) → c256(U80'(f565_in(z0), f566_in(z0), z0), F565_IN(z0))
F577_IN(z0) → c259(U81'(f585_in(z0), f586_in(z0), z0), F585_IN(z0))
F594_IN(z0) → c262(U82'(f603_in(z0), f604_in(z0), z0), F603_IN(z0))
F638_IN(z0) → c265(U83'(f647_in(z0), f648_in(z0), z0), F647_IN(z0))
F658_IN(z0) → c268(U84'(f667_in(z0), f668_in(z0), z0), F667_IN(z0))
F678_IN(z0) → c271(U85'(f687_in(z0), f688_in(z0), z0), F687_IN(z0))
F697_IN(z0) → c274(U86'(f707_in(z0), f708_in(z0), z0), F707_IN(z0))
F739_IN(z0) → c277(U87'(f748_in(z0), f749_in(z0), z0), F748_IN(z0))
F759_IN(z0) → c280(U88'(f767_in(z0), f768_in(z0), z0), F767_IN(z0))
F777_IN(z0) → c283(U89'(f784_in(z0), f785_in(z0), z0), F784_IN(z0))
F819_IN(z0) → c286(U90'(f833_in(z0), f834_in(z0), z0), F833_IN(z0))
F852_IN(z0) → c289(U91'(f863_in(z0), f864_in(z0), z0), F863_IN(z0))
F894_IN(z0) → c292(U92'(f898_in(z0), f899_in(z0), z0), F898_IN(z0))
F2_IN(z0, z1) → c1(U1'(f5_in(z0, z1), z0, z1))
F2_IN(z0, z1) → c1(F5_IN(z0, z1))
F40_IN(z0, 0) → c1(U13'(f889_in(z0), z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(U15'(f812_in(z0), z0, 0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(U18'(f733_in(z0), z0, 0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(U21'(f631_in(z0), z0, 0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(U25'(f509_in(z0), z0, 0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(U29'(f361_in(z0), z0, 0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(U34'(f193_in(z0), z0, 0))
F162_IN(z0, 0) → c1(F193_IN(z0))
S tuples:

F889_IN(z0) → c3(U2'(f894_in(z0), z0), F894_IN(z0))
F812_IN(z0) → c7(U3'(f819_in(z0), z0), F819_IN(z0))
F168_IN(z0, z1, z2) → c11(U4'(f173_in(z0, z1, z2), z0, z1, z2), F173_IN(z0, z1, z2))
F733_IN(z0) → c15(U5'(f739_in(z0), z0), F739_IN(z0))
F5_IN(z0, z1) → c19(U6'(f9_in(z0, z1), z0, z1), F9_IN(z0, z1))
F631_IN(z0) → c23(U7'(f638_in(z0), z0), F638_IN(z0))
F509_IN(z0) → c27(U8'(f517_in(z0), z0), F517_IN(z0))
F361_IN(z0) → c31(U9'(f368_in(z0), z0), F368_IN(z0))
F193_IN(z0) → c35(U10'(f201_in(z0), z0), F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(U11'(f30_in(z0, z1), s(z0), s(z1)), F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(U12'(f55_in(z0, z1), s(z0), s(z1)), F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(U14'(f74_in(z0, z1), s(z0), s(z1)), F74_IN(z0, z1))
F898_IN(s(z0)) → c54(U16'(f889_in(z0), s(z0)), F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(U17'(f94_in(z0, z1), s(z0), s(z1)), F94_IN(z0, z1))
F833_IN(s(z0)) → c63(U19'(f852_in(z0), s(z0)), F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(U20'(f113_in(z0, z1), s(z0), s(z1)), F113_IN(z0, z1))
F748_IN(s(z0)) → c73(U22'(f759_in(z0), s(z0)), F759_IN(z0))
F863_IN(s(z0)) → c76(U23'(f812_in(z0), s(z0)), F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(U24'(f133_in(z0, z1), s(z0), s(z1)), F133_IN(z0, z1))
F647_IN(s(z0)) → c85(U26'(f658_in(z0), s(z0)), F658_IN(z0))
F767_IN(s(z0)) → c89(U27'(f777_in(z0), s(z0)), F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(U28'(f153_in(z0, z1), s(z0), s(z1)), F153_IN(z0, z1))
F525_IN(s(z0)) → c99(U30'(f537_in(z0), s(z0)), F537_IN(z0))
F667_IN(s(z0)) → c103(U31'(f678_in(z0), s(z0)), F678_IN(z0))
F784_IN(s(z0)) → c106(U32'(f733_in(z0), s(z0)), F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(U33'(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1)), F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(U35'(f388_in(z0), s(z0)), F388_IN(z0))
F545_IN(s(z0)) → c117(U36'(f557_in(z0), s(z0)), F557_IN(z0))
F687_IN(s(z0)) → c121(U37'(f697_in(z0), s(z0)), F697_IN(z0))
F209_IN(s(z0)) → c125(U38'(f221_in(z0), s(z0)), F221_IN(z0))
F397_IN(s(z0)) → c129(U39'(f408_in(z0), s(z0)), F408_IN(z0))
F565_IN(s(z0)) → c133(U40'(f577_in(z0), s(z0)), F577_IN(z0))
F707_IN(s(z0)) → c136(U41'(f631_in(z0), s(z0)), F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(U42'(f168_in(z0, z1, z2), s(z0), s(z1), z2), F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(U43'(f5_in(z0, s(z1)), z0, 0, z1), F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(U44'(f241_in(z0), s(z0)), F241_IN(z0))
F417_IN(s(z0)) → c147(U45'(f428_in(z0), s(z0)), F428_IN(z0))
F585_IN(s(z0)) → c151(U46'(f594_in(z0), s(z0)), F594_IN(z0))
F249_IN(s(z0)) → c155(U47'(f261_in(z0), s(z0)), F261_IN(z0))
F437_IN(s(z0)) → c159(U48'(f453_in(z0), s(z0)), F453_IN(z0))
F603_IN(s(z0)) → c162(U49'(f509_in(z0), s(z0)), F509_IN(z0))
F269_IN(s(z0)) → c165(U50'(f280_in(z0), s(z0)), F280_IN(z0))
F459_IN(s(z0)) → c169(U51'(f472_in(z0), s(z0)), F472_IN(z0))
F289_IN(s(z0)) → c173(U52'(f300_in(z0), s(z0)), F300_IN(z0))
F479_IN(s(z0)) → c176(U53'(f361_in(z0), s(z0)), F361_IN(z0))
F309_IN(s(z0)) → c179(U54'(f320_in(z0), s(z0)), F320_IN(z0))
F329_IN(s(z0)) → c182(U55'(f193_in(z0), s(z0)), F193_IN(z0))
F9_IN(z0, z1) → c184(U56'(f18_in(z0, z1), f20_in(z0, z1), z0, z1), F18_IN(z0, z1))
F30_IN(z0, z1) → c187(U57'(f39_in(z0, z1), f40_in(z0, z1), z0, z1), F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(U58'(f61_in(z0, z1), f62_in(z0, z1), z0, z1), F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(U59'(f81_in(z0, z1), f82_in(z0, z1), z0, z1), F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(U60'(f101_in(z0, z1), f102_in(z0, z1), z0, z1), F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(U61'(f121_in(z0, z1), f122_in(z0, z1), z0, z1), F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(U62'(f141_in(z0, z1), f142_in(z0, z1), z0, z1), F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(U63'(f160_in(z0, z1), f162_in(z0, z1), z0, z1), F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(U64'(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2), F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(U65'(f209_in(z0), f211_in(z0), z0), F209_IN(z0))
F221_IN(z0) → c214(U66'(f229_in(z0), f231_in(z0), z0), F229_IN(z0))
F241_IN(z0) → c217(U67'(f249_in(z0), f251_in(z0), z0), F249_IN(z0))
F261_IN(z0) → c220(U68'(f269_in(z0), f270_in(z0), z0), F269_IN(z0))
F280_IN(z0) → c223(U69'(f289_in(z0), f290_in(z0), z0), F289_IN(z0))
F300_IN(z0) → c226(U70'(f309_in(z0), f310_in(z0), z0), F309_IN(z0))
F320_IN(z0) → c229(U71'(f329_in(z0), f330_in(z0), z0), F329_IN(z0))
F368_IN(z0) → c232(U72'(f377_in(z0), f378_in(z0), z0), F377_IN(z0))
F388_IN(z0) → c235(U73'(f397_in(z0), f398_in(z0), z0), F397_IN(z0))
F408_IN(z0) → c238(U74'(f417_in(z0), f418_in(z0), z0), F417_IN(z0))
F428_IN(z0) → c241(U75'(f437_in(z0), f438_in(z0), z0), F437_IN(z0))
F453_IN(z0) → c244(U76'(f459_in(z0), f460_in(z0), z0), F459_IN(z0))
F472_IN(z0) → c247(U77'(f479_in(z0), f480_in(z0), z0), F479_IN(z0))
F517_IN(z0) → c250(U78'(f525_in(z0), f526_in(z0), z0), F525_IN(z0))
F537_IN(z0) → c253(U79'(f545_in(z0), f546_in(z0), z0), F545_IN(z0))
F557_IN(z0) → c256(U80'(f565_in(z0), f566_in(z0), z0), F565_IN(z0))
F577_IN(z0) → c259(U81'(f585_in(z0), f586_in(z0), z0), F585_IN(z0))
F594_IN(z0) → c262(U82'(f603_in(z0), f604_in(z0), z0), F603_IN(z0))
F638_IN(z0) → c265(U83'(f647_in(z0), f648_in(z0), z0), F647_IN(z0))
F658_IN(z0) → c268(U84'(f667_in(z0), f668_in(z0), z0), F667_IN(z0))
F678_IN(z0) → c271(U85'(f687_in(z0), f688_in(z0), z0), F687_IN(z0))
F697_IN(z0) → c274(U86'(f707_in(z0), f708_in(z0), z0), F707_IN(z0))
F739_IN(z0) → c277(U87'(f748_in(z0), f749_in(z0), z0), F748_IN(z0))
F759_IN(z0) → c280(U88'(f767_in(z0), f768_in(z0), z0), F767_IN(z0))
F777_IN(z0) → c283(U89'(f784_in(z0), f785_in(z0), z0), F784_IN(z0))
F819_IN(z0) → c286(U90'(f833_in(z0), f834_in(z0), z0), F833_IN(z0))
F852_IN(z0) → c289(U91'(f863_in(z0), f864_in(z0), z0), F863_IN(z0))
F894_IN(z0) → c292(U92'(f898_in(z0), f899_in(z0), z0), F898_IN(z0))
F2_IN(z0, z1) → c1(U1'(f5_in(z0, z1), z0, z1))
F2_IN(z0, z1) → c1(F5_IN(z0, z1))
F40_IN(z0, 0) → c1(U13'(f889_in(z0), z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(U15'(f812_in(z0), z0, 0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(U18'(f733_in(z0), z0, 0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(U21'(f631_in(z0), z0, 0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(U25'(f509_in(z0), z0, 0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(U29'(f361_in(z0), z0, 0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(U34'(f193_in(z0), z0, 0))
F162_IN(z0, 0) → c1(F193_IN(z0))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F889_IN, F812_IN, F168_IN, F733_IN, F5_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F183_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F9_IN, F30_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F2_IN, F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN

Compound Symbols:

c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c184, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c1

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

Removed 92 trailing tuple parts

(40) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F2_IN(z0, z1) → c1(F5_IN(z0, z1))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F5_IN(z0, z1) → c19(F9_IN(z0, z1))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F9_IN(z0, z1) → c184(F18_IN(z0, z1))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F2_IN(z0, z1) → c1
F40_IN(z0, 0) → c1
F62_IN(z0, 0) → c1
F82_IN(z0, 0) → c1
F102_IN(z0, 0) → c1
F122_IN(z0, 0) → c1
F142_IN(z0, 0) → c1
F162_IN(z0, 0) → c1
S tuples:

F2_IN(z0, z1) → c1(F5_IN(z0, z1))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F5_IN(z0, z1) → c19(F9_IN(z0, z1))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F9_IN(z0, z1) → c184(F18_IN(z0, z1))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F2_IN(z0, z1) → c1
F40_IN(z0, 0) → c1
F62_IN(z0, 0) → c1
F82_IN(z0, 0) → c1
F102_IN(z0, 0) → c1
F122_IN(z0, 0) → c1
F142_IN(z0, 0) → c1
F162_IN(z0, 0) → c1
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F2_IN, F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F5_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F183_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F9_IN, F30_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN

Compound Symbols:

c1, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c184, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c1

(41) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

F2_IN(z0, z1) → c1(F5_IN(z0, z1))
F2_IN(z0, z1) → c1

(42) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F2_IN(z0, z1) → c1(F5_IN(z0, z1))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F5_IN(z0, z1) → c19(F9_IN(z0, z1))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F9_IN(z0, z1) → c184(F18_IN(z0, z1))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F2_IN(z0, z1) → c1
F40_IN(z0, 0) → c1
F62_IN(z0, 0) → c1
F82_IN(z0, 0) → c1
F102_IN(z0, 0) → c1
F122_IN(z0, 0) → c1
F142_IN(z0, 0) → c1
F162_IN(z0, 0) → c1
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F5_IN(z0, z1) → c19(F9_IN(z0, z1))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F9_IN(z0, z1) → c184(F18_IN(z0, z1))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F40_IN(z0, 0) → c1
F62_IN(z0, 0) → c1
F82_IN(z0, 0) → c1
F102_IN(z0, 0) → c1
F122_IN(z0, 0) → c1
F142_IN(z0, 0) → c1
F162_IN(z0, 0) → c1
K tuples:

F2_IN(z0, z1) → c1(F5_IN(z0, z1))
F2_IN(z0, z1) → c1
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F2_IN, F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F5_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F183_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F9_IN, F30_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN

Compound Symbols:

c1, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c184, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c1

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

Use forward instantiation to replace F9_IN(z0, z1) → c184(F18_IN(z0, z1)) by

F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))

(44) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F2_IN(z0, z1) → c1(F5_IN(z0, z1))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F5_IN(z0, z1) → c19(F9_IN(z0, z1))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F2_IN(z0, z1) → c1
F40_IN(z0, 0) → c1
F62_IN(z0, 0) → c1
F82_IN(z0, 0) → c1
F102_IN(z0, 0) → c1
F122_IN(z0, 0) → c1
F142_IN(z0, 0) → c1
F162_IN(z0, 0) → c1
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F5_IN(z0, z1) → c19(F9_IN(z0, z1))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F40_IN(z0, 0) → c1
F62_IN(z0, 0) → c1
F82_IN(z0, 0) → c1
F102_IN(z0, 0) → c1
F122_IN(z0, 0) → c1
F142_IN(z0, 0) → c1
F162_IN(z0, 0) → c1
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
K tuples:

F2_IN(z0, z1) → c1(F5_IN(z0, z1))
F2_IN(z0, z1) → c1
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F2_IN, F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F5_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F183_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F30_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN

Compound Symbols:

c1, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c1, c184

(45) CdtGraphRemoveDanglingProof (ComplexityIfPolyImplication transformation)

Removed 2 of 100 dangling nodes:

F2_IN(z0, z1) → c1(F5_IN(z0, z1))
F2_IN(z0, z1) → c1

(46) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F5_IN(z0, z1) → c19(F9_IN(z0, z1))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F40_IN(z0, 0) → c1
F62_IN(z0, 0) → c1
F82_IN(z0, 0) → c1
F102_IN(z0, 0) → c1
F122_IN(z0, 0) → c1
F142_IN(z0, 0) → c1
F162_IN(z0, 0) → c1
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F5_IN(z0, z1) → c19(F9_IN(z0, z1))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F40_IN(z0, 0) → c1
F62_IN(z0, 0) → c1
F82_IN(z0, 0) → c1
F102_IN(z0, 0) → c1
F122_IN(z0, 0) → c1
F142_IN(z0, 0) → c1
F162_IN(z0, 0) → c1
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F5_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F183_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F30_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN

Compound Symbols:

c1, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c1, c184

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

Split RHS of tuples not part of any SCC

(48) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F5_IN(z0, z1) → c19(F9_IN(z0, z1))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F5_IN(z0, z1) → c19(F9_IN(z0, z1))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F5_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F183_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F30_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN

Compound Symbols:

c1, c3, c7, c11, c15, c19, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184

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

Use forward instantiation to replace F5_IN(z0, z1) → c19(F9_IN(z0, z1)) by

F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))

(50) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1)))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F183_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F30_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c140, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19

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

Use forward instantiation to replace F183_IN(z0, 0, z1) → c140(F5_IN(z0, s(z1))) by

F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))

(52) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F30_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c187, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140

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

Use forward instantiation to replace F30_IN(z0, z1) → c187(F39_IN(z0, z1), F40_IN(z0, z1)) by

F30_IN(z0, 0) → c187(F39_IN(z0, 0), F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)), F40_IN(s(y0), s(y1)))

(54) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c187(F39_IN(z0, 0), F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)), F40_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c187(F39_IN(z0, 0), F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)), F40_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c187

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

Split RHS of tuples not part of any SCC

(56) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)), F40_IN(s(y0), s(y1)))
F30_IN(z0, 0) → c(F39_IN(z0, 0))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)), F40_IN(s(y0), s(y1)))
F30_IN(z0, 0) → c(F39_IN(z0, 0))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c187, c

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

Removed 2 trailing tuple parts

(58) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F30_IN(z0, 0) → c
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F30_IN(z0, 0) → c
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F18_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c39, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c

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

Use forward instantiation to replace F18_IN(s(z0), s(z1)) → c39(F30_IN(z0, z1)) by

F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))

(60) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F30_IN(z0, 0) → c
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F30_IN(z0, 0) → c
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c, c39

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

Split RHS of tuples not part of any SCC

(62) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F55_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c190, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39

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

Use forward instantiation to replace F55_IN(z0, z1) → c190(F61_IN(z0, z1), F62_IN(z0, z1)) by

F55_IN(z0, 0) → c190(F61_IN(z0, 0), F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)), F62_IN(s(y0), s(y1)))

(64) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c190(F61_IN(z0, 0), F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)), F62_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c190(F61_IN(z0, 0), F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)), F62_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c190

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

Split RHS of tuples not part of any SCC

(66) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)), F62_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F61_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)), F62_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F61_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c190, c2

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

Removed 2 trailing tuple parts

(68) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F39_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c43, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c2

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

Use forward instantiation to replace F39_IN(s(z0), s(z1)) → c43(F55_IN(z0, z1)) by

F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))

(70) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c2, c43

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

Split RHS of tuples not part of any SCC

(72) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F74_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c193, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43

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

Use forward instantiation to replace F74_IN(z0, z1) → c193(F81_IN(z0, z1), F82_IN(z0, z1)) by

F74_IN(z0, 0) → c193(F81_IN(z0, 0), F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)), F82_IN(s(y0), s(y1)))

(74) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c193(F81_IN(z0, 0), F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)), F82_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c193(F81_IN(z0, 0), F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)), F82_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c193

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

Split RHS of tuples not part of any SCC

(76) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)), F82_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F81_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)), F82_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F81_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c193, c4

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

Removed 2 trailing tuple parts

(78) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F61_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c49, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c4

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

Use forward instantiation to replace F61_IN(s(z0), s(z1)) → c49(F74_IN(z0, z1)) by

F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))

(80) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c4, c49

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

Split RHS of tuples not part of any SCC

(82) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F94_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c196, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49

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

Use forward instantiation to replace F94_IN(z0, z1) → c196(F101_IN(z0, z1), F102_IN(z0, z1)) by

F94_IN(z0, 0) → c196(F101_IN(z0, 0), F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)), F102_IN(s(y0), s(y1)))

(84) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c196(F101_IN(z0, 0), F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)), F102_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c196(F101_IN(z0, 0), F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)), F102_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c196

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

Split RHS of tuples not part of any SCC

(86) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)), F102_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F101_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)), F102_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F101_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c196, c5

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

Removed 2 trailing tuple parts

(88) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F81_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c57, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c5

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

Use forward instantiation to replace F81_IN(s(z0), s(z1)) → c57(F94_IN(z0, z1)) by

F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))

(90) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c5, c57

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

Split RHS of tuples not part of any SCC

(92) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F113_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c199, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57

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

Use forward instantiation to replace F113_IN(z0, z1) → c199(F121_IN(z0, z1), F122_IN(z0, z1)) by

F113_IN(z0, 0) → c199(F121_IN(z0, 0), F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)), F122_IN(s(y0), s(y1)))

(94) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c199(F121_IN(z0, 0), F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)), F122_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c199(F121_IN(z0, 0), F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)), F122_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c199

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

Split RHS of tuples not part of any SCC

(96) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)), F122_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F121_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)), F122_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F121_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c199, c6

(97) CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

(98) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F101_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c67, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c6

(99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID) transformation)

Use forward instantiation to replace F101_IN(s(z0), s(z1)) → c67(F113_IN(z0, z1)) by

F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))

(100) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c6, c67

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

Split RHS of tuples not part of any SCC

(102) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F133_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c202, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67

(103) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID) transformation)

Use forward instantiation to replace F133_IN(z0, z1) → c202(F141_IN(z0, z1), F142_IN(z0, z1)) by

F133_IN(z0, 0) → c202(F141_IN(z0, 0), F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)), F142_IN(s(y0), s(y1)))

(104) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c202(F141_IN(z0, 0), F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)), F142_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c202(F141_IN(z0, 0), F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)), F142_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c202

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

Split RHS of tuples not part of any SCC

(106) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)), F142_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F141_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)), F142_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F141_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c202, c8

(107) CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

(108) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F121_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c79, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c8

(109) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID) transformation)

Use forward instantiation to replace F121_IN(s(z0), s(z1)) → c79(F133_IN(z0, z1)) by

F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))

(110) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c8, c79

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

Split RHS of tuples not part of any SCC

(112) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F153_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c205, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79

(113) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID) transformation)

Use forward instantiation to replace F153_IN(z0, z1) → c205(F160_IN(z0, z1), F162_IN(z0, z1)) by

F153_IN(z0, 0) → c205(F160_IN(z0, 0), F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)), F162_IN(s(y0), s(y1)))

(114) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c205(F160_IN(z0, 0), F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)), F162_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c205(F160_IN(z0, 0), F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)), F162_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c205

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

Split RHS of tuples not part of any SCC

(116) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)), F162_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F160_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)), F162_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F160_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c205, c9

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

Removed 2 trailing tuple parts

(118) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F141_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c93, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c9

(119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID) transformation)

Use forward instantiation to replace F141_IN(s(z0), s(z1)) → c93(F153_IN(z0, z1)) by

F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))

(120) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c9, c93

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

Split RHS of tuples not part of any SCC

(122) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F173_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c208, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93

(123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID) transformation)

Use forward instantiation to replace F173_IN(z0, z1, z2) → c208(F181_IN(z0, z1, z2), F183_IN(z0, z1, z2)) by

F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2), F183_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F181_IN(s(y0), 0, z2), F183_IN(s(y0), 0, z2))

(124) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2), F183_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F181_IN(s(y0), 0, z2), F183_IN(s(y0), 0, z2))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2), F183_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F181_IN(s(y0), 0, z2), F183_IN(s(y0), 0, z2))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(125) CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID) transformation)

Removed 2 trailing tuple parts

(126) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
K tuples:none
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(127) 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.

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
We considered the (Usable) Rules:none
And the Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0   
POL(F101_IN(x1, x2)) = [1]   
POL(F102_IN(x1, x2)) = 0   
POL(F113_IN(x1, x2)) = [1]   
POL(F121_IN(x1, x2)) = [1]   
POL(F122_IN(x1, x2)) = 0   
POL(F133_IN(x1, x2)) = [1]   
POL(F141_IN(x1, x2)) = [1]   
POL(F142_IN(x1, x2)) = 0   
POL(F153_IN(x1, x2)) = [1]   
POL(F160_IN(x1, x2)) = [1]   
POL(F162_IN(x1, x2)) = 0   
POL(F168_IN(x1, x2, x3)) = [1]   
POL(F173_IN(x1, x2, x3)) = [1]   
POL(F181_IN(x1, x2, x3)) = [1]   
POL(F183_IN(x1, x2, x3)) = [1]   
POL(F18_IN(x1, x2)) = [1]   
POL(F193_IN(x1)) = 0   
POL(F201_IN(x1)) = 0   
POL(F209_IN(x1)) = 0   
POL(F221_IN(x1)) = 0   
POL(F229_IN(x1)) = 0   
POL(F241_IN(x1)) = 0   
POL(F249_IN(x1)) = 0   
POL(F261_IN(x1)) = 0   
POL(F269_IN(x1)) = 0   
POL(F280_IN(x1)) = 0   
POL(F289_IN(x1)) = 0   
POL(F300_IN(x1)) = 0   
POL(F309_IN(x1)) = 0   
POL(F30_IN(x1, x2)) = [1]   
POL(F320_IN(x1)) = 0   
POL(F329_IN(x1)) = 0   
POL(F361_IN(x1)) = 0   
POL(F368_IN(x1)) = 0   
POL(F377_IN(x1)) = 0   
POL(F388_IN(x1)) = 0   
POL(F397_IN(x1)) = 0   
POL(F39_IN(x1, x2)) = [1]   
POL(F408_IN(x1)) = 0   
POL(F40_IN(x1, x2)) = 0   
POL(F417_IN(x1)) = 0   
POL(F428_IN(x1)) = 0   
POL(F437_IN(x1)) = 0   
POL(F453_IN(x1)) = 0   
POL(F459_IN(x1)) = 0   
POL(F472_IN(x1)) = 0   
POL(F479_IN(x1)) = 0   
POL(F509_IN(x1)) = 0   
POL(F517_IN(x1)) = 0   
POL(F525_IN(x1)) = 0   
POL(F537_IN(x1)) = 0   
POL(F545_IN(x1)) = 0   
POL(F557_IN(x1)) = 0   
POL(F55_IN(x1, x2)) = [1]   
POL(F565_IN(x1)) = 0   
POL(F577_IN(x1)) = 0   
POL(F585_IN(x1)) = 0   
POL(F594_IN(x1)) = 0   
POL(F5_IN(x1, x2)) = [1]   
POL(F603_IN(x1)) = 0   
POL(F61_IN(x1, x2)) = [1]   
POL(F62_IN(x1, x2)) = 0   
POL(F631_IN(x1)) = 0   
POL(F638_IN(x1)) = 0   
POL(F647_IN(x1)) = 0   
POL(F658_IN(x1)) = 0   
POL(F667_IN(x1)) = 0   
POL(F678_IN(x1)) = 0   
POL(F687_IN(x1)) = 0   
POL(F697_IN(x1)) = 0   
POL(F707_IN(x1)) = 0   
POL(F733_IN(x1)) = 0   
POL(F739_IN(x1)) = 0   
POL(F748_IN(x1)) = 0   
POL(F74_IN(x1, x2)) = [1]   
POL(F759_IN(x1)) = 0   
POL(F767_IN(x1)) = 0   
POL(F777_IN(x1)) = 0   
POL(F784_IN(x1)) = 0   
POL(F812_IN(x1)) = 0   
POL(F819_IN(x1)) = 0   
POL(F81_IN(x1, x2)) = [1]   
POL(F82_IN(x1, x2)) = 0   
POL(F833_IN(x1)) = 0   
POL(F852_IN(x1)) = 0   
POL(F863_IN(x1)) = 0   
POL(F889_IN(x1)) = 0   
POL(F894_IN(x1)) = 0   
POL(F898_IN(x1)) = 0   
POL(F94_IN(x1, x2)) = [1]   
POL(F9_IN(x1, x2)) = [1]   
POL(c(x1)) = x1   
POL(c1(x1)) = x1   
POL(c103(x1)) = x1   
POL(c106(x1)) = x1   
POL(c108(x1)) = x1   
POL(c11(x1)) = x1   
POL(c113(x1)) = x1   
POL(c117(x1)) = x1   
POL(c121(x1)) = x1   
POL(c125(x1)) = x1   
POL(c129(x1)) = x1   
POL(c133(x1)) = x1   
POL(c136(x1)) = x1   
POL(c138(x1)) = x1   
POL(c140(x1)) = x1   
POL(c143(x1)) = x1   
POL(c147(x1)) = x1   
POL(c15(x1)) = x1   
POL(c151(x1)) = x1   
POL(c155(x1)) = x1   
POL(c159(x1)) = x1   
POL(c162(x1)) = x1   
POL(c165(x1)) = x1   
POL(c169(x1)) = x1   
POL(c173(x1)) = x1   
POL(c176(x1)) = x1   
POL(c179(x1)) = x1   
POL(c182(x1)) = x1   
POL(c184(x1)) = x1   
POL(c187(x1)) = x1   
POL(c19(x1)) = x1   
POL(c190(x1)) = x1   
POL(c193(x1)) = x1   
POL(c196(x1)) = x1   
POL(c199(x1)) = x1   
POL(c2(x1)) = x1   
POL(c202(x1)) = x1   
POL(c205(x1)) = x1   
POL(c208(x1)) = x1   
POL(c211(x1)) = x1   
POL(c214(x1)) = x1   
POL(c217(x1)) = x1   
POL(c220(x1)) = x1   
POL(c223(x1)) = x1   
POL(c226(x1)) = x1   
POL(c229(x1)) = x1   
POL(c23(x1)) = x1   
POL(c232(x1)) = x1   
POL(c235(x1)) = x1   
POL(c238(x1)) = x1   
POL(c241(x1)) = x1   
POL(c244(x1)) = x1   
POL(c247(x1)) = x1   
POL(c250(x1)) = x1   
POL(c253(x1)) = x1   
POL(c256(x1)) = x1   
POL(c259(x1)) = x1   
POL(c262(x1)) = x1   
POL(c265(x1)) = x1   
POL(c268(x1)) = x1   
POL(c27(x1)) = x1   
POL(c271(x1)) = x1   
POL(c274(x1)) = x1   
POL(c277(x1)) = x1   
POL(c280(x1)) = x1   
POL(c283(x1)) = x1   
POL(c286(x1)) = x1   
POL(c289(x1)) = x1   
POL(c292(x1)) = x1   
POL(c3(x1)) = x1   
POL(c31(x1)) = x1   
POL(c35(x1)) = x1   
POL(c39(x1)) = x1   
POL(c4(x1)) = x1   
POL(c43(x1)) = x1   
POL(c49(x1)) = x1   
POL(c5(x1)) = x1   
POL(c54(x1)) = x1   
POL(c57(x1)) = x1   
POL(c6(x1)) = x1   
POL(c63(x1)) = x1   
POL(c67(x1)) = x1   
POL(c7(x1)) = x1   
POL(c73(x1)) = x1   
POL(c76(x1)) = x1   
POL(c79(x1)) = x1   
POL(c8(x1)) = x1   
POL(c85(x1)) = x1   
POL(c89(x1)) = x1   
POL(c9(x1)) = x1   
POL(c93(x1)) = x1   
POL(c99(x1)) = x1   
POL(s(x1)) = 0   

(128) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
K tuples:

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(129) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))

(130) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
K tuples:

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(131) 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.

F898_IN(s(z0)) → c54(F889_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
We considered the (Usable) Rules:none
And the Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0   
POL(F101_IN(x1, x2)) = [2] + [2]x1   
POL(F102_IN(x1, x2)) = [3]   
POL(F113_IN(x1, x2)) = [1] + [2]x1   
POL(F121_IN(x1, x2)) = [2]x1   
POL(F122_IN(x1, x2)) = [1] + x1   
POL(F133_IN(x1, x2)) = [2]x1   
POL(F141_IN(x1, x2)) = [2]x1   
POL(F142_IN(x1, x2)) = [2]x1   
POL(F153_IN(x1, x2)) = [3] + [2]x1   
POL(F160_IN(x1, x2)) = [2]x1   
POL(F162_IN(x1, x2)) = 0   
POL(F168_IN(x1, x2, x3)) = [2]x1   
POL(F173_IN(x1, x2, x3)) = [2]x1   
POL(F181_IN(x1, x2, x3)) = [2]x1   
POL(F183_IN(x1, x2, x3)) = [2]x1   
POL(F18_IN(x1, x2)) = [2]x1   
POL(F193_IN(x1)) = 0   
POL(F201_IN(x1)) = 0   
POL(F209_IN(x1)) = 0   
POL(F221_IN(x1)) = 0   
POL(F229_IN(x1)) = 0   
POL(F241_IN(x1)) = 0   
POL(F249_IN(x1)) = 0   
POL(F261_IN(x1)) = 0   
POL(F269_IN(x1)) = 0   
POL(F280_IN(x1)) = 0   
POL(F289_IN(x1)) = 0   
POL(F300_IN(x1)) = 0   
POL(F309_IN(x1)) = 0   
POL(F30_IN(x1, x2)) = [2]x1   
POL(F320_IN(x1)) = 0   
POL(F329_IN(x1)) = 0   
POL(F361_IN(x1)) = [2]x1   
POL(F368_IN(x1)) = [2]x1   
POL(F377_IN(x1)) = [2]x1   
POL(F388_IN(x1)) = [3] + [2]x1   
POL(F397_IN(x1)) = [2] + [2]x1   
POL(F39_IN(x1, x2)) = [2]x1   
POL(F408_IN(x1)) = [2]x1   
POL(F40_IN(x1, x2)) = [2]x1   
POL(F417_IN(x1)) = [2]x1   
POL(F428_IN(x1)) = [2]x1   
POL(F437_IN(x1)) = [2]x1   
POL(F453_IN(x1)) = [3] + [2]x1   
POL(F459_IN(x1)) = [2] + [2]x1   
POL(F472_IN(x1)) = [3] + [2]x1   
POL(F479_IN(x1)) = [2] + [2]x1   
POL(F509_IN(x1)) = [1] + x1   
POL(F517_IN(x1)) = [1] + x1   
POL(F525_IN(x1)) = x1   
POL(F537_IN(x1)) = [1] + x1   
POL(F545_IN(x1)) = x1   
POL(F557_IN(x1)) = [2] + x1   
POL(F55_IN(x1, x2)) = [2]x1   
POL(F565_IN(x1)) = x1   
POL(F577_IN(x1)) = x1   
POL(F585_IN(x1)) = x1   
POL(F594_IN(x1)) = x1   
POL(F5_IN(x1, x2)) = [2]x1   
POL(F603_IN(x1)) = x1   
POL(F61_IN(x1, x2)) = [2]x1   
POL(F62_IN(x1, x2)) = x1   
POL(F631_IN(x1)) = 0   
POL(F638_IN(x1)) = 0   
POL(F647_IN(x1)) = 0   
POL(F658_IN(x1)) = 0   
POL(F667_IN(x1)) = 0   
POL(F678_IN(x1)) = 0   
POL(F687_IN(x1)) = 0   
POL(F697_IN(x1)) = 0   
POL(F707_IN(x1)) = 0   
POL(F733_IN(x1)) = 0   
POL(F739_IN(x1)) = 0   
POL(F748_IN(x1)) = 0   
POL(F74_IN(x1, x2)) = [2] + [2]x1   
POL(F759_IN(x1)) = 0   
POL(F767_IN(x1)) = 0   
POL(F777_IN(x1)) = 0   
POL(F784_IN(x1)) = 0   
POL(F812_IN(x1)) = 0   
POL(F819_IN(x1)) = 0   
POL(F81_IN(x1, x2)) = [1] + [2]x1   
POL(F82_IN(x1, x2)) = [2] + [2]x1   
POL(F833_IN(x1)) = 0   
POL(F852_IN(x1)) = 0   
POL(F863_IN(x1)) = 0   
POL(F889_IN(x1)) = [2]x1   
POL(F894_IN(x1)) = [2]x1   
POL(F898_IN(x1)) = [2]x1   
POL(F94_IN(x1, x2)) = [3] + [2]x1   
POL(F9_IN(x1, x2)) = [2]x1   
POL(c(x1)) = x1   
POL(c1(x1)) = x1   
POL(c103(x1)) = x1   
POL(c106(x1)) = x1   
POL(c108(x1)) = x1   
POL(c11(x1)) = x1   
POL(c113(x1)) = x1   
POL(c117(x1)) = x1   
POL(c121(x1)) = x1   
POL(c125(x1)) = x1   
POL(c129(x1)) = x1   
POL(c133(x1)) = x1   
POL(c136(x1)) = x1   
POL(c138(x1)) = x1   
POL(c140(x1)) = x1   
POL(c143(x1)) = x1   
POL(c147(x1)) = x1   
POL(c15(x1)) = x1   
POL(c151(x1)) = x1   
POL(c155(x1)) = x1   
POL(c159(x1)) = x1   
POL(c162(x1)) = x1   
POL(c165(x1)) = x1   
POL(c169(x1)) = x1   
POL(c173(x1)) = x1   
POL(c176(x1)) = x1   
POL(c179(x1)) = x1   
POL(c182(x1)) = x1   
POL(c184(x1)) = x1   
POL(c187(x1)) = x1   
POL(c19(x1)) = x1   
POL(c190(x1)) = x1   
POL(c193(x1)) = x1   
POL(c196(x1)) = x1   
POL(c199(x1)) = x1   
POL(c2(x1)) = x1   
POL(c202(x1)) = x1   
POL(c205(x1)) = x1   
POL(c208(x1)) = x1   
POL(c211(x1)) = x1   
POL(c214(x1)) = x1   
POL(c217(x1)) = x1   
POL(c220(x1)) = x1   
POL(c223(x1)) = x1   
POL(c226(x1)) = x1   
POL(c229(x1)) = x1   
POL(c23(x1)) = x1   
POL(c232(x1)) = x1   
POL(c235(x1)) = x1   
POL(c238(x1)) = x1   
POL(c241(x1)) = x1   
POL(c244(x1)) = x1   
POL(c247(x1)) = x1   
POL(c250(x1)) = x1   
POL(c253(x1)) = x1   
POL(c256(x1)) = x1   
POL(c259(x1)) = x1   
POL(c262(x1)) = x1   
POL(c265(x1)) = x1   
POL(c268(x1)) = x1   
POL(c27(x1)) = x1   
POL(c271(x1)) = x1   
POL(c274(x1)) = x1   
POL(c277(x1)) = x1   
POL(c280(x1)) = x1   
POL(c283(x1)) = x1   
POL(c286(x1)) = x1   
POL(c289(x1)) = x1   
POL(c292(x1)) = x1   
POL(c3(x1)) = x1   
POL(c31(x1)) = x1   
POL(c35(x1)) = x1   
POL(c39(x1)) = x1   
POL(c4(x1)) = x1   
POL(c43(x1)) = x1   
POL(c49(x1)) = x1   
POL(c5(x1)) = x1   
POL(c54(x1)) = x1   
POL(c57(x1)) = x1   
POL(c6(x1)) = x1   
POL(c63(x1)) = x1   
POL(c67(x1)) = x1   
POL(c7(x1)) = x1   
POL(c73(x1)) = x1   
POL(c76(x1)) = x1   
POL(c79(x1)) = x1   
POL(c8(x1)) = x1   
POL(c85(x1)) = x1   
POL(c89(x1)) = x1   
POL(c9(x1)) = x1   
POL(c93(x1)) = x1   
POL(c99(x1)) = x1   
POL(s(x1)) = [2] + x1   

(132) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F229_IN(s(z0)) → c143(F241_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
K tuples:

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(133) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

F889_IN(z0) → c3(F894_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
F894_IN(z0) → c292(F898_IN(z0))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
F517_IN(z0) → c250(F525_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F377_IN(s(z0)) → c113(F388_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))

(134) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F812_IN(z0) → c7(F819_IN(z0))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F229_IN(s(z0)) → c143(F241_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
K tuples:

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F889_IN(z0) → c3(F894_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(135) 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.

F647_IN(s(z0)) → c85(F658_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
We considered the (Usable) Rules:none
And the Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0   
POL(F101_IN(x1, x2)) = [2]x1   
POL(F102_IN(x1, x2)) = [2] + x1   
POL(F113_IN(x1, x2)) = [2]x1   
POL(F121_IN(x1, x2)) = [2]x1   
POL(F122_IN(x1, x2)) = [2]x1   
POL(F133_IN(x1, x2)) = [2] + [2]x1   
POL(F141_IN(x1, x2)) = [2]x1   
POL(F142_IN(x1, x2)) = [2] + [2]x1   
POL(F153_IN(x1, x2)) = [2]x1   
POL(F160_IN(x1, x2)) = [2]x1   
POL(F162_IN(x1, x2)) = x1   
POL(F168_IN(x1, x2, x3)) = [2]x1   
POL(F173_IN(x1, x2, x3)) = [2]x1   
POL(F181_IN(x1, x2, x3)) = [2]x1   
POL(F183_IN(x1, x2, x3)) = [2]x1   
POL(F18_IN(x1, x2)) = [2]x1   
POL(F193_IN(x1)) = 0   
POL(F201_IN(x1)) = 0   
POL(F209_IN(x1)) = 0   
POL(F221_IN(x1)) = 0   
POL(F229_IN(x1)) = 0   
POL(F241_IN(x1)) = 0   
POL(F249_IN(x1)) = 0   
POL(F261_IN(x1)) = 0   
POL(F269_IN(x1)) = 0   
POL(F280_IN(x1)) = 0   
POL(F289_IN(x1)) = 0   
POL(F300_IN(x1)) = 0   
POL(F309_IN(x1)) = 0   
POL(F30_IN(x1, x2)) = [3] + [2]x1   
POL(F320_IN(x1)) = 0   
POL(F329_IN(x1)) = 0   
POL(F361_IN(x1)) = [1] + x1   
POL(F368_IN(x1)) = x1   
POL(F377_IN(x1)) = x1   
POL(F388_IN(x1)) = [1] + x1   
POL(F397_IN(x1)) = [1] + x1   
POL(F39_IN(x1, x2)) = [2]x1   
POL(F408_IN(x1)) = [3] + x1   
POL(F40_IN(x1, x2)) = [2] + [2]x1   
POL(F417_IN(x1)) = x1   
POL(F428_IN(x1)) = [1] + x1   
POL(F437_IN(x1)) = [1] + x1   
POL(F453_IN(x1)) = [1] + x1   
POL(F459_IN(x1)) = x1   
POL(F472_IN(x1)) = x1   
POL(F479_IN(x1)) = x1   
POL(F509_IN(x1)) = 0   
POL(F517_IN(x1)) = 0   
POL(F525_IN(x1)) = 0   
POL(F537_IN(x1)) = 0   
POL(F545_IN(x1)) = 0   
POL(F557_IN(x1)) = 0   
POL(F55_IN(x1, x2)) = [2]x1   
POL(F565_IN(x1)) = 0   
POL(F577_IN(x1)) = 0   
POL(F585_IN(x1)) = 0   
POL(F594_IN(x1)) = 0   
POL(F5_IN(x1, x2)) = [2]x1   
POL(F603_IN(x1)) = 0   
POL(F61_IN(x1, x2)) = [2]x1   
POL(F62_IN(x1, x2)) = [2]x1   
POL(F631_IN(x1)) = [2] + x1   
POL(F638_IN(x1)) = [2] + x1   
POL(F647_IN(x1)) = x1   
POL(F658_IN(x1)) = [1] + x1   
POL(F667_IN(x1)) = x1   
POL(F678_IN(x1)) = [2] + x1   
POL(F687_IN(x1)) = x1   
POL(F697_IN(x1)) = x1   
POL(F707_IN(x1)) = x1   
POL(F733_IN(x1)) = 0   
POL(F739_IN(x1)) = 0   
POL(F748_IN(x1)) = 0   
POL(F74_IN(x1, x2)) = [2]x1   
POL(F759_IN(x1)) = 0   
POL(F767_IN(x1)) = 0   
POL(F777_IN(x1)) = 0   
POL(F784_IN(x1)) = 0   
POL(F812_IN(x1)) = 0   
POL(F819_IN(x1)) = 0   
POL(F81_IN(x1, x2)) = [2]x1   
POL(F82_IN(x1, x2)) = 0   
POL(F833_IN(x1)) = 0   
POL(F852_IN(x1)) = 0   
POL(F863_IN(x1)) = 0   
POL(F889_IN(x1)) = [2] + [2]x1   
POL(F894_IN(x1)) = [2]x1   
POL(F898_IN(x1)) = [2]x1   
POL(F94_IN(x1, x2)) = [2] + [2]x1   
POL(F9_IN(x1, x2)) = [2]x1   
POL(c(x1)) = x1   
POL(c1(x1)) = x1   
POL(c103(x1)) = x1   
POL(c106(x1)) = x1   
POL(c108(x1)) = x1   
POL(c11(x1)) = x1   
POL(c113(x1)) = x1   
POL(c117(x1)) = x1   
POL(c121(x1)) = x1   
POL(c125(x1)) = x1   
POL(c129(x1)) = x1   
POL(c133(x1)) = x1   
POL(c136(x1)) = x1   
POL(c138(x1)) = x1   
POL(c140(x1)) = x1   
POL(c143(x1)) = x1   
POL(c147(x1)) = x1   
POL(c15(x1)) = x1   
POL(c151(x1)) = x1   
POL(c155(x1)) = x1   
POL(c159(x1)) = x1   
POL(c162(x1)) = x1   
POL(c165(x1)) = x1   
POL(c169(x1)) = x1   
POL(c173(x1)) = x1   
POL(c176(x1)) = x1   
POL(c179(x1)) = x1   
POL(c182(x1)) = x1   
POL(c184(x1)) = x1   
POL(c187(x1)) = x1   
POL(c19(x1)) = x1   
POL(c190(x1)) = x1   
POL(c193(x1)) = x1   
POL(c196(x1)) = x1   
POL(c199(x1)) = x1   
POL(c2(x1)) = x1   
POL(c202(x1)) = x1   
POL(c205(x1)) = x1   
POL(c208(x1)) = x1   
POL(c211(x1)) = x1   
POL(c214(x1)) = x1   
POL(c217(x1)) = x1   
POL(c220(x1)) = x1   
POL(c223(x1)) = x1   
POL(c226(x1)) = x1   
POL(c229(x1)) = x1   
POL(c23(x1)) = x1   
POL(c232(x1)) = x1   
POL(c235(x1)) = x1   
POL(c238(x1)) = x1   
POL(c241(x1)) = x1   
POL(c244(x1)) = x1   
POL(c247(x1)) = x1   
POL(c250(x1)) = x1   
POL(c253(x1)) = x1   
POL(c256(x1)) = x1   
POL(c259(x1)) = x1   
POL(c262(x1)) = x1   
POL(c265(x1)) = x1   
POL(c268(x1)) = x1   
POL(c27(x1)) = x1   
POL(c271(x1)) = x1   
POL(c274(x1)) = x1   
POL(c277(x1)) = x1   
POL(c280(x1)) = x1   
POL(c283(x1)) = x1   
POL(c286(x1)) = x1   
POL(c289(x1)) = x1   
POL(c292(x1)) = x1   
POL(c3(x1)) = x1   
POL(c31(x1)) = x1   
POL(c35(x1)) = x1   
POL(c39(x1)) = x1   
POL(c4(x1)) = x1   
POL(c43(x1)) = x1   
POL(c49(x1)) = x1   
POL(c5(x1)) = x1   
POL(c54(x1)) = x1   
POL(c57(x1)) = x1   
POL(c6(x1)) = x1   
POL(c63(x1)) = x1   
POL(c67(x1)) = x1   
POL(c7(x1)) = x1   
POL(c73(x1)) = x1   
POL(c76(x1)) = x1   
POL(c79(x1)) = x1   
POL(c8(x1)) = x1   
POL(c85(x1)) = x1   
POL(c89(x1)) = x1   
POL(c9(x1)) = x1   
POL(c93(x1)) = x1   
POL(c99(x1)) = x1   
POL(s(x1)) = [2] + x1   

(136) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F812_IN(z0) → c7(F819_IN(z0))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F229_IN(s(z0)) → c143(F241_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
K tuples:

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F889_IN(z0) → c3(F894_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F647_IN(s(z0)) → c85(F658_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(137) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

F667_IN(s(z0)) → c103(F678_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))

(138) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F812_IN(z0) → c7(F819_IN(z0))
F733_IN(z0) → c15(F739_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F229_IN(s(z0)) → c143(F241_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
K tuples:

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F889_IN(z0) → c3(F894_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F647_IN(s(z0)) → c85(F658_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(139) 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.

F833_IN(s(z0)) → c63(F852_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
We considered the (Usable) Rules:none
And the Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0   
POL(F101_IN(x1, x2)) = [2]x1   
POL(F102_IN(x1, x2)) = [2]x1   
POL(F113_IN(x1, x2)) = [2]x1   
POL(F121_IN(x1, x2)) = [2]x1   
POL(F122_IN(x1, x2)) = 0   
POL(F133_IN(x1, x2)) = [3] + [2]x1   
POL(F141_IN(x1, x2)) = [2]x1   
POL(F142_IN(x1, x2)) = [3] + [2]x1   
POL(F153_IN(x1, x2)) = [2]x1   
POL(F160_IN(x1, x2)) = [2]x1   
POL(F162_IN(x1, x2)) = 0   
POL(F168_IN(x1, x2, x3)) = [3] + [2]x1   
POL(F173_IN(x1, x2, x3)) = [2] + [2]x1   
POL(F181_IN(x1, x2, x3)) = [2] + [2]x1   
POL(F183_IN(x1, x2, x3)) = [2] + [2]x1   
POL(F18_IN(x1, x2)) = [2]x1   
POL(F193_IN(x1)) = 0   
POL(F201_IN(x1)) = 0   
POL(F209_IN(x1)) = 0   
POL(F221_IN(x1)) = 0   
POL(F229_IN(x1)) = 0   
POL(F241_IN(x1)) = 0   
POL(F249_IN(x1)) = 0   
POL(F261_IN(x1)) = 0   
POL(F269_IN(x1)) = 0   
POL(F280_IN(x1)) = 0   
POL(F289_IN(x1)) = 0   
POL(F300_IN(x1)) = 0   
POL(F309_IN(x1)) = 0   
POL(F30_IN(x1, x2)) = [2] + [2]x1   
POL(F320_IN(x1)) = 0   
POL(F329_IN(x1)) = 0   
POL(F361_IN(x1)) = [3] + [2]x1   
POL(F368_IN(x1)) = [3] + [2]x1   
POL(F377_IN(x1)) = [2] + [2]x1   
POL(F388_IN(x1)) = [1] + [2]x1   
POL(F397_IN(x1)) = [1] + [2]x1   
POL(F39_IN(x1, x2)) = [2]x1   
POL(F408_IN(x1)) = [2] + [2]x1   
POL(F40_IN(x1, x2)) = [1] + [2]x1   
POL(F417_IN(x1)) = [1] + [2]x1   
POL(F428_IN(x1)) = [2]x1   
POL(F437_IN(x1)) = [2]x1   
POL(F453_IN(x1)) = [2] + [2]x1   
POL(F459_IN(x1)) = [2] + [2]x1   
POL(F472_IN(x1)) = [3] + [2]x1   
POL(F479_IN(x1)) = [2] + [2]x1   
POL(F509_IN(x1)) = 0   
POL(F517_IN(x1)) = 0   
POL(F525_IN(x1)) = 0   
POL(F537_IN(x1)) = 0   
POL(F545_IN(x1)) = 0   
POL(F557_IN(x1)) = 0   
POL(F55_IN(x1, x2)) = [1] + [2]x1   
POL(F565_IN(x1)) = 0   
POL(F577_IN(x1)) = 0   
POL(F585_IN(x1)) = 0   
POL(F594_IN(x1)) = 0   
POL(F5_IN(x1, x2)) = [1] + [2]x1   
POL(F603_IN(x1)) = 0   
POL(F61_IN(x1, x2)) = [2]x1   
POL(F62_IN(x1, x2)) = [1] + [2]x1   
POL(F631_IN(x1)) = 0   
POL(F638_IN(x1)) = 0   
POL(F647_IN(x1)) = 0   
POL(F658_IN(x1)) = 0   
POL(F667_IN(x1)) = 0   
POL(F678_IN(x1)) = 0   
POL(F687_IN(x1)) = 0   
POL(F697_IN(x1)) = 0   
POL(F707_IN(x1)) = 0   
POL(F733_IN(x1)) = 0   
POL(F739_IN(x1)) = 0   
POL(F748_IN(x1)) = 0   
POL(F74_IN(x1, x2)) = [2] + [2]x1   
POL(F759_IN(x1)) = 0   
POL(F767_IN(x1)) = 0   
POL(F777_IN(x1)) = 0   
POL(F784_IN(x1)) = 0   
POL(F812_IN(x1)) = [2]x1   
POL(F819_IN(x1)) = [2]x1   
POL(F81_IN(x1, x2)) = [2]x1   
POL(F82_IN(x1, x2)) = [1] + [2]x1   
POL(F833_IN(x1)) = [2]x1   
POL(F852_IN(x1)) = [3] + [2]x1   
POL(F863_IN(x1)) = [2]x1   
POL(F889_IN(x1)) = [1] + [2]x1   
POL(F894_IN(x1)) = [1] + [2]x1   
POL(F898_IN(x1)) = [2]x1   
POL(F94_IN(x1, x2)) = [3] + [2]x1   
POL(F9_IN(x1, x2)) = [1] + [2]x1   
POL(c(x1)) = x1   
POL(c1(x1)) = x1   
POL(c103(x1)) = x1   
POL(c106(x1)) = x1   
POL(c108(x1)) = x1   
POL(c11(x1)) = x1   
POL(c113(x1)) = x1   
POL(c117(x1)) = x1   
POL(c121(x1)) = x1   
POL(c125(x1)) = x1   
POL(c129(x1)) = x1   
POL(c133(x1)) = x1   
POL(c136(x1)) = x1   
POL(c138(x1)) = x1   
POL(c140(x1)) = x1   
POL(c143(x1)) = x1   
POL(c147(x1)) = x1   
POL(c15(x1)) = x1   
POL(c151(x1)) = x1   
POL(c155(x1)) = x1   
POL(c159(x1)) = x1   
POL(c162(x1)) = x1   
POL(c165(x1)) = x1   
POL(c169(x1)) = x1   
POL(c173(x1)) = x1   
POL(c176(x1)) = x1   
POL(c179(x1)) = x1   
POL(c182(x1)) = x1   
POL(c184(x1)) = x1   
POL(c187(x1)) = x1   
POL(c19(x1)) = x1   
POL(c190(x1)) = x1   
POL(c193(x1)) = x1   
POL(c196(x1)) = x1   
POL(c199(x1)) = x1   
POL(c2(x1)) = x1   
POL(c202(x1)) = x1   
POL(c205(x1)) = x1   
POL(c208(x1)) = x1   
POL(c211(x1)) = x1   
POL(c214(x1)) = x1   
POL(c217(x1)) = x1   
POL(c220(x1)) = x1   
POL(c223(x1)) = x1   
POL(c226(x1)) = x1   
POL(c229(x1)) = x1   
POL(c23(x1)) = x1   
POL(c232(x1)) = x1   
POL(c235(x1)) = x1   
POL(c238(x1)) = x1   
POL(c241(x1)) = x1   
POL(c244(x1)) = x1   
POL(c247(x1)) = x1   
POL(c250(x1)) = x1   
POL(c253(x1)) = x1   
POL(c256(x1)) = x1   
POL(c259(x1)) = x1   
POL(c262(x1)) = x1   
POL(c265(x1)) = x1   
POL(c268(x1)) = x1   
POL(c27(x1)) = x1   
POL(c271(x1)) = x1   
POL(c274(x1)) = x1   
POL(c277(x1)) = x1   
POL(c280(x1)) = x1   
POL(c283(x1)) = x1   
POL(c286(x1)) = x1   
POL(c289(x1)) = x1   
POL(c292(x1)) = x1   
POL(c3(x1)) = x1   
POL(c31(x1)) = x1   
POL(c35(x1)) = x1   
POL(c39(x1)) = x1   
POL(c4(x1)) = x1   
POL(c43(x1)) = x1   
POL(c49(x1)) = x1   
POL(c5(x1)) = x1   
POL(c54(x1)) = x1   
POL(c57(x1)) = x1   
POL(c6(x1)) = x1   
POL(c63(x1)) = x1   
POL(c67(x1)) = x1   
POL(c7(x1)) = x1   
POL(c73(x1)) = x1   
POL(c76(x1)) = x1   
POL(c79(x1)) = x1   
POL(c8(x1)) = x1   
POL(c85(x1)) = x1   
POL(c89(x1)) = x1   
POL(c9(x1)) = x1   
POL(c93(x1)) = x1   
POL(c99(x1)) = x1   
POL(s(x1)) = [2] + x1   

(140) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F812_IN(z0) → c7(F819_IN(z0))
F733_IN(z0) → c15(F739_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F229_IN(s(z0)) → c143(F241_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
K tuples:

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F889_IN(z0) → c3(F894_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F647_IN(s(z0)) → c85(F658_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(141) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

F812_IN(z0) → c7(F819_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))

(142) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F733_IN(z0) → c15(F739_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F229_IN(s(z0)) → c143(F241_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
K tuples:

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F889_IN(z0) → c3(F894_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F647_IN(s(z0)) → c85(F658_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(143) 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.

F193_IN(z0) → c35(F201_IN(z0))
F229_IN(s(z0)) → c143(F241_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
We considered the (Usable) Rules:none
And the Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = [1]   
POL(F101_IN(x1, x2)) = [2] + [2]x1   
POL(F102_IN(x1, x2)) = [2]x1 + [2]x2   
POL(F113_IN(x1, x2)) = [2] + [2]x1   
POL(F121_IN(x1, x2)) = [2] + [2]x1   
POL(F122_IN(x1, x2)) = [2] + x1   
POL(F133_IN(x1, x2)) = [2] + [2]x1   
POL(F141_IN(x1, x2)) = [2] + [2]x1   
POL(F142_IN(x1, x2)) = [2] + x1   
POL(F153_IN(x1, x2)) = [3] + [2]x1   
POL(F160_IN(x1, x2)) = [2]x1   
POL(F162_IN(x1, x2)) = [2]x1 + x2   
POL(F168_IN(x1, x2, x3)) = [2] + [2]x1   
POL(F173_IN(x1, x2, x3)) = [2] + [2]x1   
POL(F181_IN(x1, x2, x3)) = [2]x1   
POL(F183_IN(x1, x2, x3)) = [2]x1 + x2   
POL(F18_IN(x1, x2)) = [2]x1   
POL(F193_IN(x1)) = [1] + [2]x1   
POL(F201_IN(x1)) = [2]x1   
POL(F209_IN(x1)) = [2]x1   
POL(F221_IN(x1)) = [2] + [2]x1   
POL(F229_IN(x1)) = [1] + [2]x1   
POL(F241_IN(x1)) = [2] + [2]x1   
POL(F249_IN(x1)) = [2] + [2]x1   
POL(F261_IN(x1)) = [2]x1   
POL(F269_IN(x1)) = [2]x1   
POL(F280_IN(x1)) = [2] + [2]x1   
POL(F289_IN(x1)) = [2] + [2]x1   
POL(F300_IN(x1)) = [2]x1   
POL(F309_IN(x1)) = [2]x1   
POL(F30_IN(x1, x2)) = [2] + [2]x1   
POL(F320_IN(x1)) = [2]x1   
POL(F329_IN(x1)) = [2]x1   
POL(F361_IN(x1)) = [1] + x1   
POL(F368_IN(x1)) = [1] + x1   
POL(F377_IN(x1)) = [1] + x1   
POL(F388_IN(x1)) = [2] + x1   
POL(F397_IN(x1)) = x1   
POL(F39_IN(x1, x2)) = [2] + [2]x1   
POL(F408_IN(x1)) = x1   
POL(F40_IN(x1, x2)) = [2]   
POL(F417_IN(x1)) = x1   
POL(F428_IN(x1)) = [1] + x1   
POL(F437_IN(x1)) = [1] + x1   
POL(F453_IN(x1)) = [1] + x1   
POL(F459_IN(x1)) = [1] + x1   
POL(F472_IN(x1)) = [2] + x1   
POL(F479_IN(x1)) = x1   
POL(F509_IN(x1)) = [2] + x1   
POL(F517_IN(x1)) = [2] + x1   
POL(F525_IN(x1)) = [2] + x1   
POL(F537_IN(x1)) = [3] + x1   
POL(F545_IN(x1)) = [3] + x1   
POL(F557_IN(x1)) = [3] + x1   
POL(F55_IN(x1, x2)) = [2] + [2]x1   
POL(F565_IN(x1)) = [2] + x1   
POL(F577_IN(x1)) = [2] + x1   
POL(F585_IN(x1)) = [1] + x1   
POL(F594_IN(x1)) = [1] + x1   
POL(F5_IN(x1, x2)) = [1] + [2]x1   
POL(F603_IN(x1)) = [1] + x1   
POL(F61_IN(x1, x2)) = [2] + [2]x1   
POL(F62_IN(x1, x2)) = [1] + x1 + x2   
POL(F631_IN(x1)) = [1] + [2]x1   
POL(F638_IN(x1)) = [2]x1   
POL(F647_IN(x1)) = [2]x1   
POL(F658_IN(x1)) = [2] + [2]x1   
POL(F667_IN(x1)) = [2] + [2]x1   
POL(F678_IN(x1)) = [3] + [2]x1   
POL(F687_IN(x1)) = [3] + [2]x1   
POL(F697_IN(x1)) = [2]x1   
POL(F707_IN(x1)) = [2]x1   
POL(F733_IN(x1)) = 0   
POL(F739_IN(x1)) = 0   
POL(F748_IN(x1)) = 0   
POL(F74_IN(x1, x2)) = [2] + [2]x1   
POL(F759_IN(x1)) = 0   
POL(F767_IN(x1)) = 0   
POL(F777_IN(x1)) = 0   
POL(F784_IN(x1)) = 0   
POL(F812_IN(x1)) = 0   
POL(F819_IN(x1)) = 0   
POL(F81_IN(x1, x2)) = [2] + [2]x1   
POL(F82_IN(x1, x2)) = x1 + [2]x2   
POL(F833_IN(x1)) = 0   
POL(F852_IN(x1)) = 0   
POL(F863_IN(x1)) = 0   
POL(F889_IN(x1)) = 0   
POL(F894_IN(x1)) = 0   
POL(F898_IN(x1)) = 0   
POL(F94_IN(x1, x2)) = [2] + [2]x1   
POL(F9_IN(x1, x2)) = [1] + [2]x1   
POL(c(x1)) = x1   
POL(c1(x1)) = x1   
POL(c103(x1)) = x1   
POL(c106(x1)) = x1   
POL(c108(x1)) = x1   
POL(c11(x1)) = x1   
POL(c113(x1)) = x1   
POL(c117(x1)) = x1   
POL(c121(x1)) = x1   
POL(c125(x1)) = x1   
POL(c129(x1)) = x1   
POL(c133(x1)) = x1   
POL(c136(x1)) = x1   
POL(c138(x1)) = x1   
POL(c140(x1)) = x1   
POL(c143(x1)) = x1   
POL(c147(x1)) = x1   
POL(c15(x1)) = x1   
POL(c151(x1)) = x1   
POL(c155(x1)) = x1   
POL(c159(x1)) = x1   
POL(c162(x1)) = x1   
POL(c165(x1)) = x1   
POL(c169(x1)) = x1   
POL(c173(x1)) = x1   
POL(c176(x1)) = x1   
POL(c179(x1)) = x1   
POL(c182(x1)) = x1   
POL(c184(x1)) = x1   
POL(c187(x1)) = x1   
POL(c19(x1)) = x1   
POL(c190(x1)) = x1   
POL(c193(x1)) = x1   
POL(c196(x1)) = x1   
POL(c199(x1)) = x1   
POL(c2(x1)) = x1   
POL(c202(x1)) = x1   
POL(c205(x1)) = x1   
POL(c208(x1)) = x1   
POL(c211(x1)) = x1   
POL(c214(x1)) = x1   
POL(c217(x1)) = x1   
POL(c220(x1)) = x1   
POL(c223(x1)) = x1   
POL(c226(x1)) = x1   
POL(c229(x1)) = x1   
POL(c23(x1)) = x1   
POL(c232(x1)) = x1   
POL(c235(x1)) = x1   
POL(c238(x1)) = x1   
POL(c241(x1)) = x1   
POL(c244(x1)) = x1   
POL(c247(x1)) = x1   
POL(c250(x1)) = x1   
POL(c253(x1)) = x1   
POL(c256(x1)) = x1   
POL(c259(x1)) = x1   
POL(c262(x1)) = x1   
POL(c265(x1)) = x1   
POL(c268(x1)) = x1   
POL(c27(x1)) = x1   
POL(c271(x1)) = x1   
POL(c274(x1)) = x1   
POL(c277(x1)) = x1   
POL(c280(x1)) = x1   
POL(c283(x1)) = x1   
POL(c286(x1)) = x1   
POL(c289(x1)) = x1   
POL(c292(x1)) = x1   
POL(c3(x1)) = x1   
POL(c31(x1)) = x1   
POL(c35(x1)) = x1   
POL(c39(x1)) = x1   
POL(c4(x1)) = x1   
POL(c43(x1)) = x1   
POL(c49(x1)) = x1   
POL(c5(x1)) = x1   
POL(c54(x1)) = x1   
POL(c57(x1)) = x1   
POL(c6(x1)) = x1   
POL(c63(x1)) = x1   
POL(c67(x1)) = x1   
POL(c7(x1)) = x1   
POL(c73(x1)) = x1   
POL(c76(x1)) = x1   
POL(c79(x1)) = x1   
POL(c8(x1)) = x1   
POL(c85(x1)) = x1   
POL(c89(x1)) = x1   
POL(c9(x1)) = x1   
POL(c93(x1)) = x1   
POL(c99(x1)) = x1   
POL(s(x1)) = [1] + x1   

(144) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F733_IN(z0) → c15(F739_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
K tuples:

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F889_IN(z0) → c3(F894_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F647_IN(s(z0)) → c85(F658_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F229_IN(s(z0)) → c143(F241_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(145) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

F201_IN(z0) → c211(F209_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))

(146) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F733_IN(z0) → c15(F739_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
K tuples:

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F889_IN(z0) → c3(F894_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F647_IN(s(z0)) → c85(F658_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F229_IN(s(z0)) → c143(F241_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(147) 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.

F748_IN(s(z0)) → c73(F759_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
We considered the (Usable) Rules:none
And the Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
The order we found is given by the following interpretation:
Polynomial interpretation :

POL(0) = 0   
POL(F101_IN(x1, x2)) = [2]x1   
POL(F102_IN(x1, x2)) = [1] + x1   
POL(F113_IN(x1, x2)) = [2] + [2]x1   
POL(F121_IN(x1, x2)) = [2] + [2]x1   
POL(F122_IN(x1, x2)) = 0   
POL(F133_IN(x1, x2)) = [1] + [2]x1   
POL(F141_IN(x1, x2)) = [2]x1   
POL(F142_IN(x1, x2)) = [1]   
POL(F153_IN(x1, x2)) = [2]x1   
POL(F160_IN(x1, x2)) = [2]x1   
POL(F162_IN(x1, x2)) = [2]x1   
POL(F168_IN(x1, x2, x3)) = [2] + [2]x1   
POL(F173_IN(x1, x2, x3)) = [2] + [2]x1   
POL(F181_IN(x1, x2, x3)) = [1] + [2]x1   
POL(F183_IN(x1, x2, x3)) = [2] + [2]x1   
POL(F18_IN(x1, x2)) = [2] + [2]x1   
POL(F193_IN(x1)) = 0   
POL(F201_IN(x1)) = 0   
POL(F209_IN(x1)) = 0   
POL(F221_IN(x1)) = 0   
POL(F229_IN(x1)) = 0   
POL(F241_IN(x1)) = 0   
POL(F249_IN(x1)) = 0   
POL(F261_IN(x1)) = 0   
POL(F269_IN(x1)) = 0   
POL(F280_IN(x1)) = 0   
POL(F289_IN(x1)) = 0   
POL(F300_IN(x1)) = 0   
POL(F309_IN(x1)) = 0   
POL(F30_IN(x1, x2)) = [3] + [2]x1   
POL(F320_IN(x1)) = 0   
POL(F329_IN(x1)) = 0   
POL(F361_IN(x1)) = 0   
POL(F368_IN(x1)) = 0   
POL(F377_IN(x1)) = 0   
POL(F388_IN(x1)) = 0   
POL(F397_IN(x1)) = 0   
POL(F39_IN(x1, x2)) = [2] + [2]x1   
POL(F408_IN(x1)) = 0   
POL(F40_IN(x1, x2)) = [3] + [2]x1   
POL(F417_IN(x1)) = 0   
POL(F428_IN(x1)) = 0   
POL(F437_IN(x1)) = 0   
POL(F453_IN(x1)) = 0   
POL(F459_IN(x1)) = 0   
POL(F472_IN(x1)) = 0   
POL(F479_IN(x1)) = 0   
POL(F509_IN(x1)) = 0   
POL(F517_IN(x1)) = 0   
POL(F525_IN(x1)) = 0   
POL(F537_IN(x1)) = 0   
POL(F545_IN(x1)) = 0   
POL(F557_IN(x1)) = 0   
POL(F55_IN(x1, x2)) = [3] + [2]x1   
POL(F565_IN(x1)) = 0   
POL(F577_IN(x1)) = 0   
POL(F585_IN(x1)) = 0   
POL(F594_IN(x1)) = 0   
POL(F5_IN(x1, x2)) = [2] + [2]x1   
POL(F603_IN(x1)) = 0   
POL(F61_IN(x1, x2)) = [1] + [2]x1   
POL(F62_IN(x1, x2)) = [3]   
POL(F631_IN(x1)) = [1] + x1   
POL(F638_IN(x1)) = x1   
POL(F647_IN(x1)) = x1   
POL(F658_IN(x1)) = [1] + x1   
POL(F667_IN(x1)) = x1   
POL(F678_IN(x1)) = [1] + x1   
POL(F687_IN(x1)) = [1] + x1   
POL(F697_IN(x1)) = [1] + x1   
POL(F707_IN(x1)) = x1   
POL(F733_IN(x1)) = x1   
POL(F739_IN(x1)) = x1   
POL(F748_IN(x1)) = x1   
POL(F74_IN(x1, x2)) = [2] + [2]x1   
POL(F759_IN(x1)) = x1   
POL(F767_IN(x1)) = x1   
POL(F777_IN(x1)) = x1   
POL(F784_IN(x1)) = x1   
POL(F812_IN(x1)) = 0   
POL(F819_IN(x1)) = 0   
POL(F81_IN(x1, x2)) = [2]x1   
POL(F82_IN(x1, x2)) = [2] + x1   
POL(F833_IN(x1)) = 0   
POL(F852_IN(x1)) = 0   
POL(F863_IN(x1)) = 0   
POL(F889_IN(x1)) = 0   
POL(F894_IN(x1)) = 0   
POL(F898_IN(x1)) = 0   
POL(F94_IN(x1, x2)) = [1] + [2]x1   
POL(F9_IN(x1, x2)) = [2] + [2]x1   
POL(c(x1)) = x1   
POL(c1(x1)) = x1   
POL(c103(x1)) = x1   
POL(c106(x1)) = x1   
POL(c108(x1)) = x1   
POL(c11(x1)) = x1   
POL(c113(x1)) = x1   
POL(c117(x1)) = x1   
POL(c121(x1)) = x1   
POL(c125(x1)) = x1   
POL(c129(x1)) = x1   
POL(c133(x1)) = x1   
POL(c136(x1)) = x1   
POL(c138(x1)) = x1   
POL(c140(x1)) = x1   
POL(c143(x1)) = x1   
POL(c147(x1)) = x1   
POL(c15(x1)) = x1   
POL(c151(x1)) = x1   
POL(c155(x1)) = x1   
POL(c159(x1)) = x1   
POL(c162(x1)) = x1   
POL(c165(x1)) = x1   
POL(c169(x1)) = x1   
POL(c173(x1)) = x1   
POL(c176(x1)) = x1   
POL(c179(x1)) = x1   
POL(c182(x1)) = x1   
POL(c184(x1)) = x1   
POL(c187(x1)) = x1   
POL(c19(x1)) = x1   
POL(c190(x1)) = x1   
POL(c193(x1)) = x1   
POL(c196(x1)) = x1   
POL(c199(x1)) = x1   
POL(c2(x1)) = x1   
POL(c202(x1)) = x1   
POL(c205(x1)) = x1   
POL(c208(x1)) = x1   
POL(c211(x1)) = x1   
POL(c214(x1)) = x1   
POL(c217(x1)) = x1   
POL(c220(x1)) = x1   
POL(c223(x1)) = x1   
POL(c226(x1)) = x1   
POL(c229(x1)) = x1   
POL(c23(x1)) = x1   
POL(c232(x1)) = x1   
POL(c235(x1)) = x1   
POL(c238(x1)) = x1   
POL(c241(x1)) = x1   
POL(c244(x1)) = x1   
POL(c247(x1)) = x1   
POL(c250(x1)) = x1   
POL(c253(x1)) = x1   
POL(c256(x1)) = x1   
POL(c259(x1)) = x1   
POL(c262(x1)) = x1   
POL(c265(x1)) = x1   
POL(c268(x1)) = x1   
POL(c27(x1)) = x1   
POL(c271(x1)) = x1   
POL(c274(x1)) = x1   
POL(c277(x1)) = x1   
POL(c280(x1)) = x1   
POL(c283(x1)) = x1   
POL(c286(x1)) = x1   
POL(c289(x1)) = x1   
POL(c292(x1)) = x1   
POL(c3(x1)) = x1   
POL(c31(x1)) = x1   
POL(c35(x1)) = x1   
POL(c39(x1)) = x1   
POL(c4(x1)) = x1   
POL(c43(x1)) = x1   
POL(c49(x1)) = x1   
POL(c5(x1)) = x1   
POL(c54(x1)) = x1   
POL(c57(x1)) = x1   
POL(c6(x1)) = x1   
POL(c63(x1)) = x1   
POL(c67(x1)) = x1   
POL(c7(x1)) = x1   
POL(c73(x1)) = x1   
POL(c76(x1)) = x1   
POL(c79(x1)) = x1   
POL(c8(x1)) = x1   
POL(c85(x1)) = x1   
POL(c89(x1)) = x1   
POL(c9(x1)) = x1   
POL(c93(x1)) = x1   
POL(c99(x1)) = x1   
POL(s(x1)) = [1] + x1   

(148) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0, z1) → U1(f5_in(z0, z1), z0, z1)
U1(f5_out1(z0), z1, z2) → f2_out1(z0)
f889_in(0) → f889_out1(0)
f889_in(z0) → U2(f894_in(z0), z0)
U2(f894_out1(z0), z1) → f889_out1(z0)
U2(f894_out2(z0), z1) → f889_out1(z0)
f812_in(0) → f812_out1(0)
f812_in(z0) → U3(f819_in(z0), z0)
U3(f819_out1(z0), z1) → f812_out1(z0)
U3(f819_out2(z0), z1) → f812_out1(z0)
f168_in(0, s(z0), z1) → f168_out1(0)
f168_in(z0, z1, z2) → U4(f173_in(z0, z1, z2), z0, z1, z2)
U4(f173_out1(z0), z1, z2, z3) → f168_out1(z0)
U4(f173_out2(z0), z1, z2, z3) → f168_out1(z0)
f733_in(0) → f733_out1(0)
f733_in(z0) → U5(f739_in(z0), z0)
U5(f739_out1(z0), z1) → f733_out1(z0)
U5(f739_out2(z0), z1) → f733_out1(z0)
f5_in(0, s(z0)) → f5_out1(0)
f5_in(z0, z1) → U6(f9_in(z0, z1), z0, z1)
U6(f9_out1(z0), z1, z2) → f5_out1(z0)
U6(f9_out2(z0), z1, z2) → f5_out1(z0)
f631_in(0) → f631_out1(0)
f631_in(z0) → U7(f638_in(z0), z0)
U7(f638_out1(z0), z1) → f631_out1(z0)
U7(f638_out2(z0), z1) → f631_out1(z0)
f509_in(0) → f509_out1(0)
f509_in(z0) → U8(f517_in(z0), z0)
U8(f517_out1(z0), z1) → f509_out1(z0)
U8(f517_out2(z0), z1) → f509_out1(z0)
f361_in(0) → f361_out1(0)
f361_in(z0) → U9(f368_in(z0), z0)
U9(f368_out1(z0), z1) → f361_out1(z0)
U9(f368_out2(z0), z1) → f361_out1(z0)
f193_in(0) → f193_out1(0)
f193_in(z0) → U10(f201_in(z0), z0)
U10(f201_out1(z0), z1) → f193_out1(z0)
U10(f201_out2(z0), z1) → f193_out1(z0)
f18_in(s(0), s(s(z0))) → f18_out1(0)
f18_in(s(z0), s(z1)) → U11(f30_in(z0, z1), s(z0), s(z1))
U11(f30_out1(z0), s(z1), s(z2)) → f18_out1(z0)
U11(f30_out2(z0), s(z1), s(z2)) → f18_out1(z0)
f39_in(s(0), s(s(z0))) → f39_out1(0)
f39_in(s(z0), s(z1)) → U12(f55_in(z0, z1), s(z0), s(z1))
U12(f55_out1(z0), s(z1), s(z2)) → f39_out1(z0)
U12(f55_out2(z0), s(z1), s(z2)) → f39_out1(z0)
f40_in(z0, 0) → U13(f889_in(z0), z0, 0)
U13(f889_out1(z0), z1, 0) → f40_out1(s(z0))
f61_in(s(0), s(s(z0))) → f61_out1(0)
f61_in(s(z0), s(z1)) → U14(f74_in(z0, z1), s(z0), s(z1))
U14(f74_out1(z0), s(z1), s(z2)) → f61_out1(z0)
U14(f74_out2(z0), s(z1), s(z2)) → f61_out1(z0)
f62_in(z0, 0) → U15(f812_in(z0), z0, 0)
U15(f812_out1(z0), z1, 0) → f62_out1(s(z0))
f898_in(s(z0)) → U16(f889_in(z0), s(z0))
U16(f889_out1(z0), s(z1)) → f898_out1(s(z0))
f81_in(s(0), s(s(z0))) → f81_out1(0)
f81_in(s(z0), s(z1)) → U17(f94_in(z0, z1), s(z0), s(z1))
U17(f94_out1(z0), s(z1), s(z2)) → f81_out1(z0)
U17(f94_out2(z0), s(z1), s(z2)) → f81_out1(z0)
f82_in(z0, 0) → U18(f733_in(z0), z0, 0)
U18(f733_out1(z0), z1, 0) → f82_out1(s(z0))
f833_in(s(0)) → f833_out1(0)
f833_in(s(z0)) → U19(f852_in(z0), s(z0))
U19(f852_out1(z0), s(z1)) → f833_out1(z0)
U19(f852_out2(z0), s(z1)) → f833_out1(z0)
f101_in(s(0), s(s(z0))) → f101_out1(0)
f101_in(s(z0), s(z1)) → U20(f113_in(z0, z1), s(z0), s(z1))
U20(f113_out1(z0), s(z1), s(z2)) → f101_out1(z0)
U20(f113_out2(z0), s(z1), s(z2)) → f101_out1(z0)
f102_in(z0, 0) → U21(f631_in(z0), z0, 0)
U21(f631_out1(z0), z1, 0) → f102_out1(s(z0))
f748_in(s(0)) → f748_out1(0)
f748_in(s(z0)) → U22(f759_in(z0), s(z0))
U22(f759_out1(z0), s(z1)) → f748_out1(z0)
U22(f759_out2(z0), s(z1)) → f748_out1(z0)
f863_in(s(z0)) → U23(f812_in(z0), s(z0))
U23(f812_out1(z0), s(z1)) → f863_out1(s(z0))
f121_in(s(0), s(s(z0))) → f121_out1(0)
f121_in(s(z0), s(z1)) → U24(f133_in(z0, z1), s(z0), s(z1))
U24(f133_out1(z0), s(z1), s(z2)) → f121_out1(z0)
U24(f133_out2(z0), s(z1), s(z2)) → f121_out1(z0)
f122_in(z0, 0) → U25(f509_in(z0), z0, 0)
U25(f509_out1(z0), z1, 0) → f122_out1(s(z0))
f647_in(s(0)) → f647_out1(0)
f647_in(s(z0)) → U26(f658_in(z0), s(z0))
U26(f658_out1(z0), s(z1)) → f647_out1(z0)
U26(f658_out2(z0), s(z1)) → f647_out1(z0)
f767_in(s(0)) → f767_out1(0)
f767_in(s(z0)) → U27(f777_in(z0), s(z0))
U27(f777_out1(z0), s(z1)) → f767_out1(z0)
U27(f777_out2(z0), s(z1)) → f767_out1(z0)
f141_in(s(0), s(s(z0))) → f141_out1(0)
f141_in(s(z0), s(z1)) → U28(f153_in(z0, z1), s(z0), s(z1))
U28(f153_out1(z0), s(z1), s(z2)) → f141_out1(z0)
U28(f153_out2(z0), s(z1), s(z2)) → f141_out1(z0)
f142_in(z0, 0) → U29(f361_in(z0), z0, 0)
U29(f361_out1(z0), z1, 0) → f142_out1(s(z0))
f525_in(s(0)) → f525_out1(0)
f525_in(s(z0)) → U30(f537_in(z0), s(z0))
U30(f537_out1(z0), s(z1)) → f525_out1(z0)
U30(f537_out2(z0), s(z1)) → f525_out1(z0)
f667_in(s(0)) → f667_out1(0)
f667_in(s(z0)) → U31(f678_in(z0), s(z0))
U31(f678_out1(z0), s(z1)) → f667_out1(z0)
U31(f678_out2(z0), s(z1)) → f667_out1(z0)
f784_in(s(z0)) → U32(f733_in(z0), s(z0))
U32(f733_out1(z0), s(z1)) → f784_out1(s(z0))
f160_in(s(z0), s(z1)) → U33(f168_in(z0, z1, s(s(s(s(s(s(s(z1)))))))), s(z0), s(z1))
U33(f168_out1(z0), s(z1), s(z2)) → f160_out1(z0)
f162_in(z0, 0) → U34(f193_in(z0), z0, 0)
U34(f193_out1(z0), z1, 0) → f162_out1(s(z0))
f377_in(s(0)) → f377_out1(0)
f377_in(s(z0)) → U35(f388_in(z0), s(z0))
U35(f388_out1(z0), s(z1)) → f377_out1(z0)
U35(f388_out2(z0), s(z1)) → f377_out1(z0)
f545_in(s(0)) → f545_out1(0)
f545_in(s(z0)) → U36(f557_in(z0), s(z0))
U36(f557_out1(z0), s(z1)) → f545_out1(z0)
U36(f557_out2(z0), s(z1)) → f545_out1(z0)
f687_in(s(0)) → f687_out1(0)
f687_in(s(z0)) → U37(f697_in(z0), s(z0))
U37(f697_out1(z0), s(z1)) → f687_out1(z0)
U37(f697_out2(z0), s(z1)) → f687_out1(z0)
f209_in(s(0)) → f209_out1(0)
f209_in(s(z0)) → U38(f221_in(z0), s(z0))
U38(f221_out1(z0), s(z1)) → f209_out1(z0)
U38(f221_out2(z0), s(z1)) → f209_out1(z0)
f397_in(s(0)) → f397_out1(0)
f397_in(s(z0)) → U39(f408_in(z0), s(z0))
U39(f408_out1(z0), s(z1)) → f397_out1(z0)
U39(f408_out2(z0), s(z1)) → f397_out1(z0)
f565_in(s(0)) → f565_out1(0)
f565_in(s(z0)) → U40(f577_in(z0), s(z0))
U40(f577_out1(z0), s(z1)) → f565_out1(z0)
U40(f577_out2(z0), s(z1)) → f565_out1(z0)
f707_in(s(z0)) → U41(f631_in(z0), s(z0))
U41(f631_out1(z0), s(z1)) → f707_out1(s(z0))
f181_in(s(z0), s(z1), z2) → U42(f168_in(z0, z1, z2), s(z0), s(z1), z2)
U42(f168_out1(z0), s(z1), s(z2), z3) → f181_out1(z0)
f183_in(z0, 0, z1) → U43(f5_in(z0, s(z1)), z0, 0, z1)
U43(f5_out1(z0), z1, 0, z2) → f183_out1(s(z0))
f229_in(s(0)) → f229_out1(0)
f229_in(s(z0)) → U44(f241_in(z0), s(z0))
U44(f241_out1(z0), s(z1)) → f229_out1(z0)
U44(f241_out2(z0), s(z1)) → f229_out1(z0)
f417_in(s(0)) → f417_out1(0)
f417_in(s(z0)) → U45(f428_in(z0), s(z0))
U45(f428_out1(z0), s(z1)) → f417_out1(z0)
U45(f428_out2(z0), s(z1)) → f417_out1(z0)
f585_in(s(0)) → f585_out1(0)
f585_in(s(z0)) → U46(f594_in(z0), s(z0))
U46(f594_out1(z0), s(z1)) → f585_out1(z0)
U46(f594_out2(z0), s(z1)) → f585_out1(z0)
f249_in(s(0)) → f249_out1(0)
f249_in(s(z0)) → U47(f261_in(z0), s(z0))
U47(f261_out1(z0), s(z1)) → f249_out1(z0)
U47(f261_out2(z0), s(z1)) → f249_out1(z0)
f437_in(s(0)) → f437_out1(0)
f437_in(s(z0)) → U48(f453_in(z0), s(z0))
U48(f453_out1(z0), s(z1)) → f437_out1(z0)
U48(f453_out2(z0), s(z1)) → f437_out1(z0)
f603_in(s(z0)) → U49(f509_in(z0), s(z0))
U49(f509_out1(z0), s(z1)) → f603_out1(s(z0))
f269_in(s(0)) → f269_out1(0)
f269_in(s(z0)) → U50(f280_in(z0), s(z0))
U50(f280_out1(z0), s(z1)) → f269_out1(z0)
U50(f280_out2(z0), s(z1)) → f269_out1(z0)
f459_in(s(0)) → f459_out1(0)
f459_in(s(z0)) → U51(f472_in(z0), s(z0))
U51(f472_out1(z0), s(z1)) → f459_out1(z0)
U51(f472_out2(z0), s(z1)) → f459_out1(z0)
f289_in(s(0)) → f289_out1(0)
f289_in(s(z0)) → U52(f300_in(z0), s(z0))
U52(f300_out1(z0), s(z1)) → f289_out1(z0)
U52(f300_out2(z0), s(z1)) → f289_out1(z0)
f479_in(s(z0)) → U53(f361_in(z0), s(z0))
U53(f361_out1(z0), s(z1)) → f479_out1(s(z0))
f309_in(s(0)) → f309_out1(0)
f309_in(s(z0)) → U54(f320_in(z0), s(z0))
U54(f320_out1(z0), s(z1)) → f309_out1(z0)
U54(f320_out2(z0), s(z1)) → f309_out1(z0)
f329_in(s(z0)) → U55(f193_in(z0), s(z0))
U55(f193_out1(z0), s(z1)) → f329_out1(s(z0))
f9_in(z0, z1) → U56(f18_in(z0, z1), f20_in(z0, z1), z0, z1)
U56(f18_out1(z0), z1, z2, z3) → f9_out1(z0)
U56(z0, f20_out1(z1), z2, z3) → f9_out2(z1)
f30_in(z0, z1) → U57(f39_in(z0, z1), f40_in(z0, z1), z0, z1)
U57(f39_out1(z0), z1, z2, z3) → f30_out1(z0)
U57(z0, f40_out1(z1), z2, z3) → f30_out2(z1)
f55_in(z0, z1) → U58(f61_in(z0, z1), f62_in(z0, z1), z0, z1)
U58(f61_out1(z0), z1, z2, z3) → f55_out1(z0)
U58(z0, f62_out1(z1), z2, z3) → f55_out2(z1)
f74_in(z0, z1) → U59(f81_in(z0, z1), f82_in(z0, z1), z0, z1)
U59(f81_out1(z0), z1, z2, z3) → f74_out1(z0)
U59(z0, f82_out1(z1), z2, z3) → f74_out2(z1)
f94_in(z0, z1) → U60(f101_in(z0, z1), f102_in(z0, z1), z0, z1)
U60(f101_out1(z0), z1, z2, z3) → f94_out1(z0)
U60(z0, f102_out1(z1), z2, z3) → f94_out2(z1)
f113_in(z0, z1) → U61(f121_in(z0, z1), f122_in(z0, z1), z0, z1)
U61(f121_out1(z0), z1, z2, z3) → f113_out1(z0)
U61(z0, f122_out1(z1), z2, z3) → f113_out2(z1)
f133_in(z0, z1) → U62(f141_in(z0, z1), f142_in(z0, z1), z0, z1)
U62(f141_out1(z0), z1, z2, z3) → f133_out1(z0)
U62(z0, f142_out1(z1), z2, z3) → f133_out2(z1)
f153_in(z0, z1) → U63(f160_in(z0, z1), f162_in(z0, z1), z0, z1)
U63(f160_out1(z0), z1, z2, z3) → f153_out1(z0)
U63(z0, f162_out1(z1), z2, z3) → f153_out2(z1)
f173_in(z0, z1, z2) → U64(f181_in(z0, z1, z2), f183_in(z0, z1, z2), z0, z1, z2)
U64(f181_out1(z0), z1, z2, z3, z4) → f173_out1(z0)
U64(z0, f183_out1(z1), z2, z3, z4) → f173_out2(z1)
f201_in(z0) → U65(f209_in(z0), f211_in(z0), z0)
U65(f209_out1(z0), z1, z2) → f201_out1(z0)
U65(z0, f211_out1(z1), z2) → f201_out2(z1)
f221_in(z0) → U66(f229_in(z0), f231_in(z0), z0)
U66(f229_out1(z0), z1, z2) → f221_out1(z0)
U66(z0, f231_out1(z1), z2) → f221_out2(z1)
f241_in(z0) → U67(f249_in(z0), f251_in(z0), z0)
U67(f249_out1(z0), z1, z2) → f241_out1(z0)
U67(z0, f251_out1(z1), z2) → f241_out2(z1)
f261_in(z0) → U68(f269_in(z0), f270_in(z0), z0)
U68(f269_out1(z0), z1, z2) → f261_out1(z0)
U68(z0, f270_out1(z1), z2) → f261_out2(z1)
f280_in(z0) → U69(f289_in(z0), f290_in(z0), z0)
U69(f289_out1(z0), z1, z2) → f280_out1(z0)
U69(z0, f290_out1(z1), z2) → f280_out2(z1)
f300_in(z0) → U70(f309_in(z0), f310_in(z0), z0)
U70(f309_out1(z0), z1, z2) → f300_out1(z0)
U70(z0, f310_out1(z1), z2) → f300_out2(z1)
f320_in(z0) → U71(f329_in(z0), f330_in(z0), z0)
U71(f329_out1(z0), z1, z2) → f320_out1(z0)
U71(z0, f330_out1(z1), z2) → f320_out2(z1)
f368_in(z0) → U72(f377_in(z0), f378_in(z0), z0)
U72(f377_out1(z0), z1, z2) → f368_out1(z0)
U72(z0, f378_out1(z1), z2) → f368_out2(z1)
f388_in(z0) → U73(f397_in(z0), f398_in(z0), z0)
U73(f397_out1(z0), z1, z2) → f388_out1(z0)
U73(z0, f398_out1(z1), z2) → f388_out2(z1)
f408_in(z0) → U74(f417_in(z0), f418_in(z0), z0)
U74(f417_out1(z0), z1, z2) → f408_out1(z0)
U74(z0, f418_out1(z1), z2) → f408_out2(z1)
f428_in(z0) → U75(f437_in(z0), f438_in(z0), z0)
U75(f437_out1(z0), z1, z2) → f428_out1(z0)
U75(z0, f438_out1(z1), z2) → f428_out2(z1)
f453_in(z0) → U76(f459_in(z0), f460_in(z0), z0)
U76(f459_out1(z0), z1, z2) → f453_out1(z0)
U76(z0, f460_out1(z1), z2) → f453_out2(z1)
f472_in(z0) → U77(f479_in(z0), f480_in(z0), z0)
U77(f479_out1(z0), z1, z2) → f472_out1(z0)
U77(z0, f480_out1(z1), z2) → f472_out2(z1)
f517_in(z0) → U78(f525_in(z0), f526_in(z0), z0)
U78(f525_out1(z0), z1, z2) → f517_out1(z0)
U78(z0, f526_out1(z1), z2) → f517_out2(z1)
f537_in(z0) → U79(f545_in(z0), f546_in(z0), z0)
U79(f545_out1(z0), z1, z2) → f537_out1(z0)
U79(z0, f546_out1(z1), z2) → f537_out2(z1)
f557_in(z0) → U80(f565_in(z0), f566_in(z0), z0)
U80(f565_out1(z0), z1, z2) → f557_out1(z0)
U80(z0, f566_out1(z1), z2) → f557_out2(z1)
f577_in(z0) → U81(f585_in(z0), f586_in(z0), z0)
U81(f585_out1(z0), z1, z2) → f577_out1(z0)
U81(z0, f586_out1(z1), z2) → f577_out2(z1)
f594_in(z0) → U82(f603_in(z0), f604_in(z0), z0)
U82(f603_out1(z0), z1, z2) → f594_out1(z0)
U82(z0, f604_out1(z1), z2) → f594_out2(z1)
f638_in(z0) → U83(f647_in(z0), f648_in(z0), z0)
U83(f647_out1(z0), z1, z2) → f638_out1(z0)
U83(z0, f648_out1(z1), z2) → f638_out2(z1)
f658_in(z0) → U84(f667_in(z0), f668_in(z0), z0)
U84(f667_out1(z0), z1, z2) → f658_out1(z0)
U84(z0, f668_out1(z1), z2) → f658_out2(z1)
f678_in(z0) → U85(f687_in(z0), f688_in(z0), z0)
U85(f687_out1(z0), z1, z2) → f678_out1(z0)
U85(z0, f688_out1(z1), z2) → f678_out2(z1)
f697_in(z0) → U86(f707_in(z0), f708_in(z0), z0)
U86(f707_out1(z0), z1, z2) → f697_out1(z0)
U86(z0, f708_out1(z1), z2) → f697_out2(z1)
f739_in(z0) → U87(f748_in(z0), f749_in(z0), z0)
U87(f748_out1(z0), z1, z2) → f739_out1(z0)
U87(z0, f749_out1(z1), z2) → f739_out2(z1)
f759_in(z0) → U88(f767_in(z0), f768_in(z0), z0)
U88(f767_out1(z0), z1, z2) → f759_out1(z0)
U88(z0, f768_out1(z1), z2) → f759_out2(z1)
f777_in(z0) → U89(f784_in(z0), f785_in(z0), z0)
U89(f784_out1(z0), z1, z2) → f777_out1(z0)
U89(z0, f785_out1(z1), z2) → f777_out2(z1)
f819_in(z0) → U90(f833_in(z0), f834_in(z0), z0)
U90(f833_out1(z0), z1, z2) → f819_out1(z0)
U90(z0, f834_out1(z1), z2) → f819_out2(z1)
f852_in(z0) → U91(f863_in(z0), f864_in(z0), z0)
U91(f863_out1(z0), z1, z2) → f852_out1(z0)
U91(z0, f864_out1(z1), z2) → f852_out2(z1)
f894_in(z0) → U92(f898_in(z0), f899_in(z0), z0)
U92(f898_out1(z0), z1, z2) → f894_out1(z0)
U92(z0, f899_out1(z1), z2) → f894_out2(z1)
Tuples:

F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F889_IN(z0) → c3(F894_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F733_IN(z0) → c15(F739_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F647_IN(s(z0)) → c85(F658_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F229_IN(s(z0)) → c143(F241_IN(z0))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F30_IN(z0, 0) → c(F40_IN(z0, 0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
S tuples:

F733_IN(z0) → c15(F739_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
K tuples:

F30_IN(z0, 0) → c(F40_IN(z0, 0))
F55_IN(z0, 0) → c2(F62_IN(z0, 0))
F74_IN(z0, 0) → c4(F82_IN(z0, 0))
F94_IN(z0, 0) → c5(F102_IN(z0, 0))
F113_IN(z0, 0) → c6(F122_IN(z0, 0))
F133_IN(z0, 0) → c8(F142_IN(z0, 0))
F153_IN(z0, 0) → c9(F162_IN(z0, 0))
F40_IN(z0, 0) → c1(F889_IN(z0))
F62_IN(z0, 0) → c1(F812_IN(z0))
F82_IN(z0, 0) → c1(F733_IN(z0))
F102_IN(z0, 0) → c1(F631_IN(z0))
F122_IN(z0, 0) → c1(F509_IN(z0))
F142_IN(z0, 0) → c1(F361_IN(z0))
F162_IN(z0, 0) → c1(F193_IN(z0))
F898_IN(s(z0)) → c54(F889_IN(z0))
F525_IN(s(z0)) → c99(F537_IN(z0))
F160_IN(s(z0), s(z1)) → c108(F168_IN(z0, z1, s(s(s(s(s(s(s(z1)))))))))
F377_IN(s(z0)) → c113(F388_IN(z0))
F397_IN(s(z0)) → c129(F408_IN(z0))
F565_IN(s(z0)) → c133(F577_IN(z0))
F181_IN(s(z0), s(z1), z2) → c138(F168_IN(z0, z1, z2))
F417_IN(s(z0)) → c147(F428_IN(z0))
F585_IN(s(z0)) → c151(F594_IN(z0))
F437_IN(s(z0)) → c159(F453_IN(z0))
F603_IN(s(z0)) → c162(F509_IN(z0))
F459_IN(s(z0)) → c169(F472_IN(z0))
F479_IN(s(z0)) → c176(F361_IN(z0))
F388_IN(z0) → c235(F397_IN(z0))
F453_IN(z0) → c244(F459_IN(z0))
F472_IN(z0) → c247(F479_IN(z0))
F517_IN(z0) → c250(F525_IN(z0))
F537_IN(z0) → c253(F545_IN(z0))
F557_IN(z0) → c256(F565_IN(z0))
F18_IN(s(z0), s(0)) → c39(F30_IN(z0, 0))
F18_IN(s(s(y0)), s(s(y1))) → c39(F30_IN(s(y0), s(y1)))
F39_IN(s(z0), s(0)) → c43(F55_IN(z0, 0))
F39_IN(s(s(y0)), s(s(y1))) → c43(F55_IN(s(y0), s(y1)))
F74_IN(s(y0), s(y1)) → c193(F81_IN(s(y0), s(y1)))
F61_IN(s(z0), s(0)) → c49(F74_IN(z0, 0))
F61_IN(s(s(y0)), s(s(y1))) → c49(F74_IN(s(y0), s(y1)))
F94_IN(s(y0), s(y1)) → c196(F101_IN(s(y0), s(y1)))
F81_IN(s(z0), s(0)) → c57(F94_IN(z0, 0))
F81_IN(s(s(y0)), s(s(y1))) → c57(F94_IN(s(y0), s(y1)))
F113_IN(s(y0), s(y1)) → c199(F121_IN(s(y0), s(y1)))
F101_IN(s(z0), s(0)) → c67(F113_IN(z0, 0))
F101_IN(s(s(y0)), s(s(y1))) → c67(F113_IN(s(y0), s(y1)))
F121_IN(s(z0), s(0)) → c79(F133_IN(z0, 0))
F121_IN(s(s(y0)), s(s(y1))) → c79(F133_IN(s(y0), s(y1)))
F153_IN(s(y0), s(y1)) → c205(F160_IN(s(y0), s(y1)))
F141_IN(s(z0), s(0)) → c93(F153_IN(z0, 0))
F141_IN(s(s(y0)), s(s(y1))) → c93(F153_IN(s(y0), s(y1)))
F889_IN(z0) → c3(F894_IN(z0))
F168_IN(z0, z1, z2) → c11(F173_IN(z0, z1, z2))
F509_IN(z0) → c27(F517_IN(z0))
F361_IN(z0) → c31(F368_IN(z0))
F545_IN(s(z0)) → c117(F557_IN(z0))
F368_IN(z0) → c232(F377_IN(z0))
F408_IN(z0) → c238(F417_IN(z0))
F428_IN(z0) → c241(F437_IN(z0))
F577_IN(z0) → c259(F585_IN(z0))
F594_IN(z0) → c262(F603_IN(z0))
F894_IN(z0) → c292(F898_IN(z0))
F30_IN(s(y0), s(y1)) → c187(F39_IN(s(y0), s(y1)))
F55_IN(s(y0), s(y1)) → c190(F61_IN(s(y0), s(y1)))
F133_IN(s(y0), s(y1)) → c202(F141_IN(s(y0), s(y1)))
F173_IN(s(y0), s(y1), z2) → c208(F181_IN(s(y0), s(y1), z2))
F173_IN(s(y0), 0, z2) → c208(F183_IN(s(y0), 0, z2))
F183_IN(s(y0), 0, z1) → c140(F5_IN(s(y0), s(z1)))
F5_IN(s(y0), s(y1)) → c19(F9_IN(s(y0), s(y1)))
F9_IN(s(y0), s(y1)) → c184(F18_IN(s(y0), s(y1)))
F647_IN(s(z0)) → c85(F658_IN(z0))
F687_IN(s(z0)) → c121(F697_IN(z0))
F638_IN(z0) → c265(F647_IN(z0))
F658_IN(z0) → c268(F667_IN(z0))
F678_IN(z0) → c271(F687_IN(z0))
F667_IN(s(z0)) → c103(F678_IN(z0))
F697_IN(z0) → c274(F707_IN(z0))
F707_IN(s(z0)) → c136(F631_IN(z0))
F631_IN(z0) → c23(F638_IN(z0))
F833_IN(s(z0)) → c63(F852_IN(z0))
F863_IN(s(z0)) → c76(F812_IN(z0))
F852_IN(z0) → c289(F863_IN(z0))
F812_IN(z0) → c7(F819_IN(z0))
F819_IN(z0) → c286(F833_IN(z0))
F193_IN(z0) → c35(F201_IN(z0))
F229_IN(s(z0)) → c143(F241_IN(z0))
F249_IN(s(z0)) → c155(F261_IN(z0))
F289_IN(s(z0)) → c173(F300_IN(z0))
F309_IN(s(z0)) → c179(F320_IN(z0))
F329_IN(s(z0)) → c182(F193_IN(z0))
F221_IN(z0) → c214(F229_IN(z0))
F201_IN(z0) → c211(F209_IN(z0))
F241_IN(z0) → c217(F249_IN(z0))
F261_IN(z0) → c220(F269_IN(z0))
F300_IN(z0) → c226(F309_IN(z0))
F320_IN(z0) → c229(F329_IN(z0))
F209_IN(s(z0)) → c125(F221_IN(z0))
F269_IN(s(z0)) → c165(F280_IN(z0))
F280_IN(z0) → c223(F289_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
Defined Rule Symbols:

f2_in, U1, f889_in, U2, f812_in, U3, f168_in, U4, f733_in, U5, f5_in, U6, f631_in, U7, f509_in, U8, f361_in, U9, f193_in, U10, f18_in, U11, f39_in, U12, f40_in, U13, f61_in, U14, f62_in, U15, f898_in, U16, f81_in, U17, f82_in, U18, f833_in, U19, f101_in, U20, f102_in, U21, f748_in, U22, f863_in, U23, f121_in, U24, f122_in, U25, f647_in, U26, f767_in, U27, f141_in, U28, f142_in, U29, f525_in, U30, f667_in, U31, f784_in, U32, f160_in, U33, f162_in, U34, f377_in, U35, f545_in, U36, f687_in, U37, f209_in, U38, f397_in, U39, f565_in, U40, f707_in, U41, f181_in, U42, f183_in, U43, f229_in, U44, f417_in, U45, f585_in, U46, f249_in, U47, f437_in, U48, f603_in, U49, f269_in, U50, f459_in, U51, f289_in, U52, f479_in, U53, f309_in, U54, f329_in, U55, f9_in, U56, f30_in, U57, f55_in, U58, f74_in, U59, f94_in, U60, f113_in, U61, f133_in, U62, f153_in, U63, f173_in, U64, f201_in, U65, f221_in, U66, f241_in, U67, f261_in, U68, f280_in, U69, f300_in, U70, f320_in, U71, f368_in, U72, f388_in, U73, f408_in, U74, f428_in, U75, f453_in, U76, f472_in, U77, f517_in, U78, f537_in, U79, f557_in, U80, f577_in, U81, f594_in, U82, f638_in, U83, f658_in, U84, f678_in, U85, f697_in, U86, f739_in, U87, f759_in, U88, f777_in, U89, f819_in, U90, f852_in, U91, f894_in, U92

Defined Pair Symbols:

F40_IN, F62_IN, F82_IN, F102_IN, F122_IN, F142_IN, F162_IN, F889_IN, F812_IN, F168_IN, F733_IN, F631_IN, F509_IN, F361_IN, F193_IN, F898_IN, F833_IN, F748_IN, F863_IN, F647_IN, F767_IN, F525_IN, F667_IN, F784_IN, F160_IN, F377_IN, F545_IN, F687_IN, F209_IN, F397_IN, F565_IN, F707_IN, F181_IN, F229_IN, F417_IN, F585_IN, F249_IN, F437_IN, F603_IN, F269_IN, F459_IN, F289_IN, F479_IN, F309_IN, F329_IN, F201_IN, F221_IN, F241_IN, F261_IN, F280_IN, F300_IN, F320_IN, F368_IN, F388_IN, F408_IN, F428_IN, F453_IN, F472_IN, F517_IN, F537_IN, F557_IN, F577_IN, F594_IN, F638_IN, F658_IN, F678_IN, F697_IN, F739_IN, F759_IN, F777_IN, F819_IN, F852_IN, F894_IN, F9_IN, F5_IN, F183_IN, F30_IN, F18_IN, F55_IN, F39_IN, F74_IN, F61_IN, F94_IN, F81_IN, F113_IN, F101_IN, F133_IN, F121_IN, F153_IN, F141_IN, F173_IN

Compound Symbols:

c1, c3, c7, c11, c15, c23, c27, c31, c35, c54, c63, c73, c76, c85, c89, c99, c103, c106, c108, c113, c117, c121, c125, c129, c133, c136, c138, c143, c147, c151, c155, c159, c162, c165, c169, c173, c176, c179, c182, c211, c214, c217, c220, c223, c226, c229, c232, c235, c238, c241, c244, c247, c250, c253, c256, c259, c262, c265, c268, c271, c274, c277, c280, c283, c286, c289, c292, c184, c19, c140, c, c187, c39, c2, c190, c43, c4, c193, c49, c5, c196, c57, c6, c199, c67, c8, c202, c79, c9, c205, c93, c208

(149) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

F733_IN(z0) → c15(F739_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F759_IN(z0) → c280(F767_IN(z0))
F777_IN(z0) → c283(F784_IN(z0))
F739_IN(z0) → c277(F748_IN(z0))
F748_IN(s(z0)) → c73(F759_IN(z0))
F767_IN(s(z0)) → c89(F777_IN(z0))
F784_IN(s(z0)) → c106(F733_IN(z0))
Now S is empty

(150) BOUNDS(O(1), O(1))