KILLED proof of input_TDTYBleZOZ.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (10) TRS for Loop Detection (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxRelTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (18) CdtProblem (19) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CdtProblem (21) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CdtProblem (23) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxTRS (25) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (26) CpxTRS (27) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CpxWeightedTrs (29) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxTypedWeightedTrs (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) CompletionProof [UPPER BOUND(ID), 0 ms] (36) CpxTypedWeightedCompleteTrs (37) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CpxTypedWeightedCompleteTrs (39) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CpxRNTS (43) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 429 ms] (48) CdtProblem (49) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 206 ms] (50) CdtProblem (51) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 935 ms] (52) CdtProblem (53) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (144) CpxWeightedTrs (145) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CpxTypedWeightedTrs (147) CompletionProof [UPPER BOUND(ID), 0 ms] (148) CpxTypedWeightedCompleteTrs (149) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CpxTypedWeightedCompleteTrs (151) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 7 ms] (152) CpxRNTS (153) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CpxRNTS (155) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CpxRNTS (157) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (158) CpxRNTS (159) CompletionProof [UPPER BOUND(ID), 0 ms] (160) CpxTypedWeightedCompleteTrs (161) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (162) CpxRNTS ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) f(0, s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) f(0, 0, s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) f(0, 0, 0, s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) f(0, 0, 0, 0, s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) f(0, 0, 0, 0, 0, s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) f(0, 0, 0, 0, 0, 0, s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) f(0, 0, 0, 0, 0, 0, 0, s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) f(0, 0, 0, 0, 0, 0, 0, 0, s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) f(0', s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) f(0', 0', s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) f(0', 0', 0', s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) f(0', 0', 0', 0', s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) f(0', 0', 0', 0', 0', s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) f(0', 0', 0', 0', 0', 0', s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) f(0', 0', 0', 0', 0', 0', 0', s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) f(0', 0', 0', 0', 0', 0', 0', 0', s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) f(0', 0', 0', 0', 0', 0', 0', 0', 0', s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) f(0', 0', 0', 0', 0', 0', 0', 0', 0', 0') -> 0' S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) f(0, s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) f(0, 0, s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) f(0, 0, 0, s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) f(0, 0, 0, 0, s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) f(0, 0, 0, 0, 0, s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) f(0, 0, 0, 0, 0, 0, s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) f(0, 0, 0, 0, 0, 0, 0, s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) f(0, 0, 0, 0, 0, 0, 0, 0, s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: f(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> f(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9) f(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> f(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8) f(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> f(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7) f(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> f(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6) f(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> f(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5) f(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> f(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4) f(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> f(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3) f(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2) f(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1) f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0) f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 Tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> c10 S tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> c10 K tuples:none Defined Rule Symbols: f_10 Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> c10 The (relative) TRS S consists of the following rules: f(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> f(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9) f(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> f(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8) f(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> f(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7) f(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> f(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6) f(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> f(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5) f(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> f(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4) f(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> f(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3) f(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2) f(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1) f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0) f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (9) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (10) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> c10 The (relative) TRS S consists of the following rules: f(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> f(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9) f(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> f(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8) f(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> f(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7) f(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> f(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6) f(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> f(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5) f(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> f(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4) f(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> f(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3) f(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2) f(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1) f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0) f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (11) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (12) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0', s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0', 0', s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0', 0', 0', s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0', 0', 0', 0', s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0', 0', 0', 0', 0', s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0', 0', 0', 0', 0', 0', s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0', 0', 0', 0', 0', 0', 0', s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0', 0', 0', 0', 0', 0', 0', 0', s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0', 0', 0', 0', 0', 0', 0', 0', 0', s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0', 0', 0', 0', 0', 0', 0', 0', 0', 0') -> c10 The (relative) TRS S consists of the following rules: f(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> f(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9) f(0', s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> f(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8) f(0', 0', s(z0), z1, z2, z3, z4, z5, z6, z7) -> f(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7) f(0', 0', 0', s(z0), z1, z2, z3, z4, z5, z6) -> f(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6) f(0', 0', 0', 0', s(z0), z1, z2, z3, z4, z5) -> f(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5) f(0', 0', 0', 0', 0', s(z0), z1, z2, z3, z4) -> f(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4) f(0', 0', 0', 0', 0', 0', s(z0), z1, z2, z3) -> f(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3) f(0', 0', 0', 0', 0', 0', 0', s(z0), z1, z2) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2) f(0', 0', 0', 0', 0', 0', 0', 0', s(z0), z1) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1) f(0', 0', 0', 0', 0', 0', 0', 0', 0', s(z0)) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0) f(0', 0', 0', 0', 0', 0', 0', 0', 0', 0') -> 0' Rewrite Strategy: INNERMOST ---------------------------------------- (13) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (14) Obligation: Innermost TRS: Rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0', s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0', 0', s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0', 0', 0', s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0', 0', 0', 0', s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0', 0', 0', 0', 0', s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0', 0', 0', 0', 0', 0', s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0', 0', 0', 0', 0', 0', 0', s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0', 0', 0', 0', 0', 0', 0', 0', s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0', 0', 0', 0', 0', 0', 0', 0', 0', s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0', 0', 0', 0', 0', 0', 0', 0', 0', 0') -> c10 f(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> f(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9) f(0', s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> f(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8) f(0', 0', s(z0), z1, z2, z3, z4, z5, z6, z7) -> f(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7) f(0', 0', 0', s(z0), z1, z2, z3, z4, z5, z6) -> f(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6) f(0', 0', 0', 0', s(z0), z1, z2, z3, z4, z5) -> f(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5) f(0', 0', 0', 0', 0', s(z0), z1, z2, z3, z4) -> f(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4) f(0', 0', 0', 0', 0', 0', s(z0), z1, z2, z3) -> f(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3) f(0', 0', 0', 0', 0', 0', 0', s(z0), z1, z2) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2) f(0', 0', 0', 0', 0', 0', 0', 0', s(z0), z1) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1) f(0', 0', 0', 0', 0', 0', 0', 0', 0', s(z0)) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0) f(0', 0', 0', 0', 0', 0', 0', 0', 0', 0') -> 0' Types: F :: s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 s :: s:0' -> s:0' c :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 0' :: s:0' c1 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c2 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c3 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c4 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c5 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c6 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c7 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c8 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c9 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c10 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 f :: s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' hole_c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c101_11 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 hole_s:0'2_11 :: s:0' gen_c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c103_11 :: Nat -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 gen_s:0'4_11 :: Nat -> s:0' ---------------------------------------- (15) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: F, f ---------------------------------------- (16) Obligation: Innermost TRS: Rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0', s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0', 0', s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0', 0', 0', s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0', 0', 0', 0', s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0', 0', 0', 0', 0', s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0', 0', 0', 0', 0', 0', s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0', 0', 0', 0', 0', 0', 0', s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0', 0', 0', 0', 0', 0', 0', 0', s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0', 0', 0', 0', 0', 0', 0', 0', 0', s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0', 0', 0', 0', 0', 0', 0', 0', 0', 0') -> c10 f(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> f(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9) f(0', s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> f(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8) f(0', 0', s(z0), z1, z2, z3, z4, z5, z6, z7) -> f(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7) f(0', 0', 0', s(z0), z1, z2, z3, z4, z5, z6) -> f(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6) f(0', 0', 0', 0', s(z0), z1, z2, z3, z4, z5) -> f(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5) f(0', 0', 0', 0', 0', s(z0), z1, z2, z3, z4) -> f(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4) f(0', 0', 0', 0', 0', 0', s(z0), z1, z2, z3) -> f(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3) f(0', 0', 0', 0', 0', 0', 0', s(z0), z1, z2) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2) f(0', 0', 0', 0', 0', 0', 0', 0', s(z0), z1) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1) f(0', 0', 0', 0', 0', 0', 0', 0', 0', s(z0)) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0) f(0', 0', 0', 0', 0', 0', 0', 0', 0', 0') -> 0' Types: F :: s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 s :: s:0' -> s:0' c :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 0' :: s:0' c1 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c2 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c3 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c4 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c5 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c6 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c7 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c8 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c9 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 c10 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 f :: s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' -> s:0' hole_c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c101_11 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 hole_s:0'2_11 :: s:0' gen_c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c103_11 :: Nat -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c10 gen_s:0'4_11 :: Nat -> s:0' Generator Equations: gen_c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c103_11(0) <=> c10 gen_c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c103_11(+(x, 1)) <=> c(gen_c:c1:c2:c3:c4:c5:c6:c7:c8:c9:c103_11(x)) gen_s:0'4_11(0) <=> 0' gen_s:0'4_11(+(x, 1)) <=> s(gen_s:0'4_11(x)) The following defined symbols remain to be analysed: F, f ---------------------------------------- (17) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (18) Obligation: Complexity Dependency Tuples Problem Rules: f(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> f(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9) f(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> f(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8) f(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> f(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7) f(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> f(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6) f(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> f(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5) f(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> f(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4) f(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> f(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3) f(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2) f(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1) f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0) f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 Tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> c10 S tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> c10 K tuples:none Defined Rule Symbols: f_10 Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c10 ---------------------------------------- (19) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: F(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> c10 ---------------------------------------- (20) Obligation: Complexity Dependency Tuples Problem Rules: f(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> f(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9) f(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> f(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8) f(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> f(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7) f(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> f(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6) f(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> f(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5) f(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> f(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4) f(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> f(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3) f(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2) f(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1) f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0) f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 Tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) S tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) K tuples:none Defined Rule Symbols: f_10 Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (21) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: f(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> f(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9) f(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> f(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8) f(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> f(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7) f(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> f(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6) f(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> f(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5) f(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> f(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4) f(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> f(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3) f(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2) f(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1) f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> f(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0) f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 ---------------------------------------- (22) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) S tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) K tuples:none Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (23) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (24) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (25) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (26) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (27) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (28) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) [1] F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) [1] F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) [1] F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) [1] F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) [1] F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) [1] F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) [1] F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) [1] F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) [1] F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (29) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (30) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) [1] F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) [1] F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) [1] F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) [1] F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) [1] F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) [1] F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) [1] F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) [1] F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) [1] F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) [1] The TRS has the following type information: F :: s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 s :: s:0 -> s:0 c :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 0 :: s:0 c1 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c2 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c3 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c4 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c5 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c6 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c7 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c8 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c9 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 Rewrite Strategy: INNERMOST ---------------------------------------- (31) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: F(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9) -> null_F [0] And the following fresh constants: null_F ---------------------------------------- (32) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) [1] F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) [1] F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) [1] F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) [1] F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) [1] F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) [1] F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) [1] F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) [1] F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) [1] F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) [1] F(v0, v1, v2, v3, v4, v5, v6, v7, v8, v9) -> null_F [0] The TRS has the following type information: F :: s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F s :: s:0 -> s:0 c :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F 0 :: s:0 c1 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F c2 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F c3 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F c4 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F c5 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F c6 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F c7 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F c8 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F c9 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F null_F :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9:null_F Rewrite Strategy: INNERMOST ---------------------------------------- (33) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 null_F => 0 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 0 }-> 0 :|: v0 >= 0, v8 >= 0, z10 = v3, z14 = v7, v6 >= 0, z'' = v2, z11 = v4, z13 = v6, v1 >= 0, v5 >= 0, z = v0, z' = v1, z12 = v5, v2 >= 0, v3 >= 0, v4 >= 0, v7 >= 0, v9 >= 0, z15 = v8, z16 = v9 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0) :|: z'' = 0, z13 = 0, z14 = 0, z15 = 0, z0 >= 0, z12 = 0, z = 0, z11 = 0, z' = 0, z10 = 0, z16 = 1 + z0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1) :|: z'' = 0, z1 >= 0, z13 = 0, z14 = 0, z15 = 1 + z0, z0 >= 0, z12 = 0, z = 0, z11 = 0, z16 = z1, z' = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2) :|: z0 >= 0, z14 = 1 + z0, z = 0, z16 = z2, z2 >= 0, z' = 0, z'' = 0, z15 = z1, z1 >= 0, z13 = 0, z12 = 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3) :|: z13 = 1 + z0, z14 = z1, z0 >= 0, z = 0, z15 = z2, z2 >= 0, z3 >= 0, z' = 0, z'' = 0, z1 >= 0, z16 = z3, z12 = 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4) :|: z16 = z4, z0 >= 0, z4 >= 0, z = 0, z15 = z3, z2 >= 0, z3 >= 0, z' = 0, z'' = 0, z14 = z2, z1 >= 0, z13 = z1, z12 = 1 + z0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5) :|: z5 >= 0, z13 = z2, z0 >= 0, z4 >= 0, z = 0, z14 = z3, z2 >= 0, z3 >= 0, z' = 0, z'' = 0, z1 >= 0, z15 = z4, z12 = z1, z16 = z5, z11 = 1 + z0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6) :|: z5 >= 0, z11 = z1, z15 = z5, z0 >= 0, z4 >= 0, z = 0, z14 = z4, z2 >= 0, z3 >= 0, z' = 0, z'' = 0, z13 = z3, z1 >= 0, z16 = z6, z12 = z2, z6 >= 0, z10 = 1 + z0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7) :|: z5 >= 0, z12 = z3, z16 = z7, z0 >= 0, z4 >= 0, z = 0, z13 = z4, z2 >= 0, z3 >= 0, z' = 0, z'' = 1 + z0, z10 = z1, z1 >= 0, z14 = z5, z11 = z2, z15 = z6, z6 >= 0, z7 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8) :|: z5 >= 0, z10 = z2, z14 = z6, z0 >= 0, z4 >= 0, z' = 1 + z0, z = 0, z13 = z5, z2 >= 0, z3 >= 0, z'' = z1, z12 = z4, z1 >= 0, z15 = z7, z11 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z16 = z8 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9) :|: z'' = z2, z5 >= 0, z11 = z4, z15 = z8, z = 1 + z0, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z9 >= 0, z1 >= 0, z13 = z6, z10 = z3, z14 = z7, z6 >= 0, z7 >= 0, z8 >= 0, z16 = z9 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (35) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: F_10 (c) The following functions are completely defined: none Due to the following rules being added: none And the following fresh constants: const ---------------------------------------- (36) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) [1] F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) [1] F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) [1] F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) [1] F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) [1] F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) [1] F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) [1] F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) [1] F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) [1] F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) [1] The TRS has the following type information: F :: s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 s :: s:0 -> s:0 c :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 0 :: s:0 c1 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c2 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c3 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c4 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c5 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c6 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c7 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c8 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c9 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 const :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 Rewrite Strategy: INNERMOST ---------------------------------------- (37) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (38) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) [1] F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) [1] F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) [1] F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) [1] F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) [1] F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) [1] F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) [1] F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) [1] F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) [1] F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) [1] The TRS has the following type information: F :: s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 s :: s:0 -> s:0 c :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 0 :: s:0 c1 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c2 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c3 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c4 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c5 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c6 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c7 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c8 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 c9 :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 -> c:c1:c2:c3:c4:c5:c6:c7:c8:c9 const :: c:c1:c2:c3:c4:c5:c6:c7:c8:c9 Rewrite Strategy: INNERMOST ---------------------------------------- (39) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 const => 0 ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0) :|: z'' = 0, z13 = 0, z14 = 0, z15 = 0, z0 >= 0, z12 = 0, z = 0, z11 = 0, z' = 0, z10 = 0, z16 = 1 + z0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1) :|: z'' = 0, z1 >= 0, z13 = 0, z14 = 0, z15 = 1 + z0, z0 >= 0, z12 = 0, z = 0, z11 = 0, z16 = z1, z' = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2) :|: z0 >= 0, z14 = 1 + z0, z = 0, z16 = z2, z2 >= 0, z' = 0, z'' = 0, z15 = z1, z1 >= 0, z13 = 0, z12 = 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3) :|: z13 = 1 + z0, z14 = z1, z0 >= 0, z = 0, z15 = z2, z2 >= 0, z3 >= 0, z' = 0, z'' = 0, z1 >= 0, z16 = z3, z12 = 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4) :|: z16 = z4, z0 >= 0, z4 >= 0, z = 0, z15 = z3, z2 >= 0, z3 >= 0, z' = 0, z'' = 0, z14 = z2, z1 >= 0, z13 = z1, z12 = 1 + z0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5) :|: z5 >= 0, z13 = z2, z0 >= 0, z4 >= 0, z = 0, z14 = z3, z2 >= 0, z3 >= 0, z' = 0, z'' = 0, z1 >= 0, z15 = z4, z12 = z1, z16 = z5, z11 = 1 + z0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6) :|: z5 >= 0, z11 = z1, z15 = z5, z0 >= 0, z4 >= 0, z = 0, z14 = z4, z2 >= 0, z3 >= 0, z' = 0, z'' = 0, z13 = z3, z1 >= 0, z16 = z6, z12 = z2, z6 >= 0, z10 = 1 + z0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7) :|: z5 >= 0, z12 = z3, z16 = z7, z0 >= 0, z4 >= 0, z = 0, z13 = z4, z2 >= 0, z3 >= 0, z' = 0, z'' = 1 + z0, z10 = z1, z1 >= 0, z14 = z5, z11 = z2, z15 = z6, z6 >= 0, z7 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8) :|: z5 >= 0, z10 = z2, z14 = z6, z0 >= 0, z4 >= 0, z' = 1 + z0, z = 0, z13 = z5, z2 >= 0, z3 >= 0, z'' = z1, z12 = z4, z1 >= 0, z15 = z7, z11 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z16 = z8 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9) :|: z'' = z2, z5 >= 0, z11 = z4, z15 = z8, z = 1 + z0, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z9 >= 0, z1 >= 0, z13 = z6, z10 = z3, z14 = z7, z6 >= 0, z7 >= 0, z8 >= 0, z16 = z9 ---------------------------------------- (41) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (42) Obligation: Complexity RNTS consisting of the following rules: F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z - 1, z', z'', z10, z11, z12, z13, z14, z15, z16) :|: z12 >= 0, z - 1 >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z16 >= 0, z' >= 0, z13 >= 0, z14 >= 0, z15 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z' - 1, z' - 1, z'', z10, z11, z12, z13, z14, z15, z16) :|: z13 >= 0, z' - 1 >= 0, z12 >= 0, z = 0, z10 >= 0, z11 >= 0, z'' >= 0, z14 >= 0, z15 >= 0, z16 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z'' - 1, z'' - 1, z'' - 1, z10, z11, z12, z13, z14, z15, z16) :|: z14 >= 0, z'' - 1 >= 0, z13 >= 0, z = 0, z11 >= 0, z12 >= 0, z' = 0, z10 >= 0, z15 >= 0, z16 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z10 - 1, z10 - 1, z10 - 1, z10 - 1, z11, z12, z13, z14, z15, z16) :|: z15 >= 0, z10 - 1 >= 0, z14 >= 0, z = 0, z12 >= 0, z13 >= 0, z' = 0, z'' = 0, z11 >= 0, z16 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z11 - 1, z11 - 1, z11 - 1, z11 - 1, z11 - 1, z12, z13, z14, z15, z16) :|: z16 >= 0, z11 - 1 >= 0, z15 >= 0, z = 0, z13 >= 0, z14 >= 0, z' = 0, z'' = 0, z12 >= 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z12 - 1, z12 - 1, z12 - 1, z12 - 1, z12 - 1, z12 - 1, z13, z14, z15, z16) :|: z12 - 1 >= 0, z16 >= 0, z = 0, z14 >= 0, z15 >= 0, z' = 0, z'' = 0, z13 >= 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z13 - 1, z13 - 1, z13 - 1, z13 - 1, z13 - 1, z13 - 1, z13 - 1, z14, z15, z16) :|: z13 - 1 >= 0, z = 0, z15 >= 0, z16 >= 0, z' = 0, z'' = 0, z14 >= 0, z12 = 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z15, z16) :|: z14 - 1 >= 0, z = 0, z16 >= 0, z' = 0, z'' = 0, z15 >= 0, z13 = 0, z12 = 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z16) :|: z'' = 0, z16 >= 0, z13 = 0, z14 = 0, z15 - 1 >= 0, z12 = 0, z = 0, z11 = 0, z' = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1) :|: z'' = 0, z13 = 0, z14 = 0, z15 = 0, z16 - 1 >= 0, z12 = 0, z = 0, z11 = 0, z' = 0, z10 = 0 ---------------------------------------- (43) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { F } ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z - 1, z', z'', z10, z11, z12, z13, z14, z15, z16) :|: z12 >= 0, z - 1 >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z16 >= 0, z' >= 0, z13 >= 0, z14 >= 0, z15 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z' - 1, z' - 1, z'', z10, z11, z12, z13, z14, z15, z16) :|: z13 >= 0, z' - 1 >= 0, z12 >= 0, z = 0, z10 >= 0, z11 >= 0, z'' >= 0, z14 >= 0, z15 >= 0, z16 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z'' - 1, z'' - 1, z'' - 1, z10, z11, z12, z13, z14, z15, z16) :|: z14 >= 0, z'' - 1 >= 0, z13 >= 0, z = 0, z11 >= 0, z12 >= 0, z' = 0, z10 >= 0, z15 >= 0, z16 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z10 - 1, z10 - 1, z10 - 1, z10 - 1, z11, z12, z13, z14, z15, z16) :|: z15 >= 0, z10 - 1 >= 0, z14 >= 0, z = 0, z12 >= 0, z13 >= 0, z' = 0, z'' = 0, z11 >= 0, z16 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z11 - 1, z11 - 1, z11 - 1, z11 - 1, z11 - 1, z12, z13, z14, z15, z16) :|: z16 >= 0, z11 - 1 >= 0, z15 >= 0, z = 0, z13 >= 0, z14 >= 0, z' = 0, z'' = 0, z12 >= 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z12 - 1, z12 - 1, z12 - 1, z12 - 1, z12 - 1, z12 - 1, z13, z14, z15, z16) :|: z12 - 1 >= 0, z16 >= 0, z = 0, z14 >= 0, z15 >= 0, z' = 0, z'' = 0, z13 >= 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z13 - 1, z13 - 1, z13 - 1, z13 - 1, z13 - 1, z13 - 1, z13 - 1, z14, z15, z16) :|: z13 - 1 >= 0, z = 0, z15 >= 0, z16 >= 0, z' = 0, z'' = 0, z14 >= 0, z12 = 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z15, z16) :|: z14 - 1 >= 0, z = 0, z16 >= 0, z' = 0, z'' = 0, z15 >= 0, z13 = 0, z12 = 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z16) :|: z'' = 0, z16 >= 0, z13 = 0, z14 = 0, z15 - 1 >= 0, z12 = 0, z = 0, z11 = 0, z' = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1) :|: z'' = 0, z13 = 0, z14 = 0, z15 = 0, z16 - 1 >= 0, z12 = 0, z = 0, z11 = 0, z' = 0, z10 = 0 Function symbols to be analyzed: {F} ---------------------------------------- (45) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (46) Obligation: Complexity RNTS consisting of the following rules: F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z - 1, z', z'', z10, z11, z12, z13, z14, z15, z16) :|: z12 >= 0, z - 1 >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z16 >= 0, z' >= 0, z13 >= 0, z14 >= 0, z15 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z' - 1, z' - 1, z'', z10, z11, z12, z13, z14, z15, z16) :|: z13 >= 0, z' - 1 >= 0, z12 >= 0, z = 0, z10 >= 0, z11 >= 0, z'' >= 0, z14 >= 0, z15 >= 0, z16 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z'' - 1, z'' - 1, z'' - 1, z10, z11, z12, z13, z14, z15, z16) :|: z14 >= 0, z'' - 1 >= 0, z13 >= 0, z = 0, z11 >= 0, z12 >= 0, z' = 0, z10 >= 0, z15 >= 0, z16 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z10 - 1, z10 - 1, z10 - 1, z10 - 1, z11, z12, z13, z14, z15, z16) :|: z15 >= 0, z10 - 1 >= 0, z14 >= 0, z = 0, z12 >= 0, z13 >= 0, z' = 0, z'' = 0, z11 >= 0, z16 >= 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z11 - 1, z11 - 1, z11 - 1, z11 - 1, z11 - 1, z12, z13, z14, z15, z16) :|: z16 >= 0, z11 - 1 >= 0, z15 >= 0, z = 0, z13 >= 0, z14 >= 0, z' = 0, z'' = 0, z12 >= 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z12 - 1, z12 - 1, z12 - 1, z12 - 1, z12 - 1, z12 - 1, z13, z14, z15, z16) :|: z12 - 1 >= 0, z16 >= 0, z = 0, z14 >= 0, z15 >= 0, z' = 0, z'' = 0, z13 >= 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z13 - 1, z13 - 1, z13 - 1, z13 - 1, z13 - 1, z13 - 1, z13 - 1, z14, z15, z16) :|: z13 - 1 >= 0, z = 0, z15 >= 0, z16 >= 0, z' = 0, z'' = 0, z14 >= 0, z12 = 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z14 - 1, z15, z16) :|: z14 - 1 >= 0, z = 0, z16 >= 0, z' = 0, z'' = 0, z15 >= 0, z13 = 0, z12 = 0, z11 = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z15 - 1, z16) :|: z'' = 0, z16 >= 0, z13 = 0, z14 = 0, z15 - 1 >= 0, z12 = 0, z = 0, z11 = 0, z' = 0, z10 = 0 F(z, z', z'', z10, z11, z12, z13, z14, z15, z16) -{ 1 }-> 1 + F(z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1, z16 - 1) :|: z'' = 0, z13 = 0, z14 = 0, z15 = 0, z16 - 1 >= 0, z12 = 0, z = 0, z11 = 0, z' = 0, z10 = 0 Function symbols to be analyzed: {F} ---------------------------------------- (47) CdtRuleRemovalProof (UPPER BOUND(ADD(n^2))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) We considered the (Usable) Rules:none And the Tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(F(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)) = [2]x_10^2 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c4(x_1)) = x_1 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c7(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(s(x_1)) = [2] + x_1 ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) S tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (49) CdtRuleRemovalProof (UPPER BOUND(ADD(n^2))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) We considered the (Usable) Rules:none And the Tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(F(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)) = x_9 + x_10^2 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c4(x_1)) = x_1 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c7(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(s(x_1)) = [2] + x_1 ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) S tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (51) CdtRuleRemovalProof (UPPER BOUND(ADD(n^3))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) We considered the (Usable) Rules:none And the Tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) The order we found is given by the following interpretation: Polynomial interpretation : POL(0) = 0 POL(F(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)) = x_8 + x_9^2 + x_10^3 POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c2(x_1)) = x_1 POL(c3(x_1)) = x_1 POL(c4(x_1)) = x_1 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c7(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(s(x_1)) = [1] + x_1 ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) S tuples: F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (53) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(s(z0), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9)) by F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) S tuples: F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1 ---------------------------------------- (55) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, s(z0), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(z0, z0, z1, z2, z3, z4, z5, z6, z7, z8)) by F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) S tuples: F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (57) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, s(z0), z1, z2, z3, z4, z5, z6, z7) -> c2(F(z0, z0, z0, z1, z2, z3, z4, z5, z6, z7)) by F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) S tuples: F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1, c2_1 ---------------------------------------- (59) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, s(z0), z1, z2, z3, z4, z5, z6) -> c3(F(z0, z0, z0, z0, z1, z2, z3, z4, z5, z6)) by F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) S tuples: F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1, c2_1, c3_1 ---------------------------------------- (61) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, 0, s(z0), z1, z2, z3, z4, z5) -> c4(F(z0, z0, z0, z0, z0, z1, z2, z3, z4, z5)) by F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) S tuples: F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1, c2_1, c3_1, c4_1 ---------------------------------------- (63) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, 0, 0, s(z0), z1, z2, z3, z4) -> c5(F(z0, z0, z0, z0, z0, z0, z1, z2, z3, z4)) by F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) S tuples: F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c6_1, c7_1, c8_1, c9_1, c_1, c1_1, c2_1, c3_1, c4_1, c5_1 ---------------------------------------- (65) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, 0, 0, 0, s(z0), z1, z2, z3) -> c6(F(z0, z0, z0, z0, z0, z0, z0, z1, z2, z3)) by F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) S tuples: F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c7_1, c8_1, c9_1, c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1 ---------------------------------------- (67) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, 0, 0, 0, 0, s(z0), z1, z2) -> c7(F(z0, z0, z0, z0, z0, z0, z0, z0, z1, z2)) by F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) S tuples: F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c8_1, c9_1, c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1 ---------------------------------------- (69) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, 0, 0, 0, 0, 0, s(z0), z1) -> c8(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z1)) by F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) S tuples: F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) K tuples: F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c9_1, c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1 ---------------------------------------- (71) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(z0)) -> c9(F(z0, z0, z0, z0, z0, z0, z0, z0, z0, z0)) by F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) S tuples: F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (73) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(y0), z1, z2, z3, z4, z5, z6, z7, z8, z9)) by F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) S tuples: F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (75) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(0, s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) by F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) S tuples: F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (77) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(0, 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) by F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) S tuples: F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (79) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(0, 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) by F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) S tuples: F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (81) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(0, 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) by F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) S tuples: F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (83) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(0, 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) by F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) S tuples: F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (85) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(0, 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) by F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) S tuples: F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (87) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(0, 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) by F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) S tuples: F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (89) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) by F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) S tuples: F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c_1, c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1 ---------------------------------------- (91) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) by F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) S tuples: F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1 ---------------------------------------- (93) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, s(y0), z2, z3, z4, z5, z6, z7, z8)) by F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) S tuples: F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1 ---------------------------------------- (95) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, s(y0), z3, z4, z5, z6, z7, z8)) by F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) S tuples: F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1 ---------------------------------------- (97) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, s(y0), z4, z5, z6, z7, z8)) by F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) S tuples: F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1 ---------------------------------------- (99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, s(y0), z5, z6, z7, z8)) by F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) S tuples: F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1 ---------------------------------------- (101) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, s(y0), z6, z7, z8)) by F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) S tuples: F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1 ---------------------------------------- (103) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(y0), z7, z8)) by F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) S tuples: F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1 ---------------------------------------- (105) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z8)) by F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) S tuples: F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1 ---------------------------------------- (107) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) by F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) S tuples: F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1 ---------------------------------------- (109) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8)) by F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) S tuples: F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c1_1, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1 ---------------------------------------- (111) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(0), s(0), z1, z2, z3, z4, z5, z6, z7, z8)) by F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) S tuples: F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (113) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, s(y0), z2, z3, z4, z5, z6, z7)) by F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) S tuples: F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (115) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, s(y0), z3, z4, z5, z6, z7)) by F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) S tuples: F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (117) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, s(y0), z4, z5, z6, z7)) by F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) S tuples: F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, s(y0), z5, z6, z7)) by F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) S tuples: F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (121) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(y0), z6, z7)) by F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) S tuples: F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z7)) by F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) S tuples: F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (125) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) by F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) S tuples: F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (127) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6, z7)) by F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) S tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (129) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, s(y0), z2, z3, z4, z5, z6)) by F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) S tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (131) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, s(y0), z3, z4, z5, z6)) by F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) S tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (133) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, s(y0), z4, z5, z6)) by F(0, 0, 0, s(0), 0, 0, s(0), s(y0), z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, s(y0), z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, 0, s(0), s(y0), z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, s(y0), z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) S tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, 0, s(0), s(y0), z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, s(y0), z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (135) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(y0), z5, z6)) by F(0, 0, 0, s(0), 0, 0, 0, s(0), s(y0), z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, 0, s(0), 0, 0, 0, s(0), 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, 0, s(0), s(y0), z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, s(y0), z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, 0, s(0), s(y0), z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, 0, s(0), 0, 0, 0, s(0), 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) S tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, 0, s(0), s(y0), z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, s(y0), z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, 0, s(0), s(y0), z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, 0, s(0), 0, 0, 0, s(0), 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (137) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z6)) by F(0, 0, 0, s(0), 0, 0, 0, 0, s(0), s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, 0, s(0), s(y0), z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, s(y0), z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, 0, s(0), s(y0), z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, 0, s(0), 0, 0, 0, s(0), 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(0), s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) S tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, 0, s(0), s(y0), z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, s(y0), z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, 0, s(0), s(y0), z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, 0, s(0), 0, 0, 0, s(0), 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(0), s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (139) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) by F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0)))) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(s(0))) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, 0, s(0), s(y0), z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, s(y0), z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, 0, s(0), s(y0), z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, 0, s(0), 0, 0, 0, s(0), 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(0), s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0)))) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(s(0))) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) S tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, 0, s(0), s(y0), z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, s(y0), z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, 0, s(0), s(y0), z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, 0, s(0), 0, 0, 0, s(0), 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(0), s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0)))) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(s(0))) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (141) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5, z6)) by F(0, 0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(0)), s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules:none Tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, 0, s(0), s(y0), z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, s(y0), z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, 0, s(0), s(y0), z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, 0, s(0), 0, 0, 0, s(0), 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(0), s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0)))) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(s(0))) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(0)), s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6)) S tuples: F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(0), s(0), s(0), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c3(F(s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, s(y0), z2, z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, s(y0), z3, z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, s(y0), z4, z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z5)) F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c4(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c4(F(s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4, z5)) F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, s(y0), z2, z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, s(y0), z3, z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z4)) F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c5(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c5(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c5(F(s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3, z4)) F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, s(y0), z2, z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z3)) F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c6(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c6(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2, z3)) F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c6(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2, z3)) F(s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(s(y0)), z1, z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), s(y0), z2, z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), s(y0), z2, z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, s(y0), z3, z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, s(y0), z3, z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, s(y0), z4, z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, s(y0), z4, z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, s(y0), z5, z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, s(y0), z5, z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, s(y0), z6, z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, s(y0), z6, z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, s(y0), z7, z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, s(y0), z7, z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z8, z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, s(y0), z8, z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0), z9) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, s(y0), z9)) F(s(s(0)), 0, 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), s(y0), z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, s(y0), z3, z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, s(y0), z4, z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, s(y0), z5, z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, s(y0), z6, z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7, z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, s(y0), z7, z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z8) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, s(y0), z8)) F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8) -> c(F(0, s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(s(0), 0, s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(s(0), 0, 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(s(0), 0, 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(s(0), 0, 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(s(0), 0, 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(s(0), 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(0), s(0), s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(y0))) F(0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6, z7) -> c1(F(0, 0, s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, s(0), 0, s(0), s(y0), z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, s(y0), z3, z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, s(y0), z4, z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, s(y0), z5, z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, s(y0), z6) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, s(0), 0, s(0), 0, 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5, z6) -> c1(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, s(0), 0, 0, s(0), s(y0), z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, s(y0), z3, z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, s(y0), z4, z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, s(y0), z5) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, s(0), 0, 0, s(0), 0, 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4, z5) -> c1(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, s(0), 0, 0, 0, s(0), s(y0), z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, s(y0), z3, z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, s(y0), z4) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, s(0), 0, 0, 0, s(0), 0, 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3, z4) -> c1(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, s(0), 0, 0, 0, 0, s(0), s(y0), z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, s(y0), z3) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, s(0), 0, 0, 0, 0, s(0), 0, 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2, z3) -> c1(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, s(0), 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, s(0), 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c1(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, s(0), 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c1(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7, z8) -> c1(F(s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7, z8)) F(0, s(s(0)), s(y0), z1, z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), s(y0), z1, z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, s(y0), z2, z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, s(y0), z2, z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, s(y0), z3, z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, s(y0), z3, z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, s(y0), z4, z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, s(y0), z4, z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, s(y0), z5, z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, s(y0), z5, z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, s(y0), z6, z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, s(y0), z6, z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, s(y0), z7) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, s(y0), z7)) F(0, s(s(0)), 0, 0, 0, 0, 0, 0, 0, s(y0)) -> c1(F(s(0), s(0), 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(0), s(y0), z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), s(y0), z2, z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, s(y0), z3, z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, s(y0), z3, z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, s(y0), z4, z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, s(y0), z4, z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, s(y0), z5, z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, s(y0), z5, z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, s(y0), z6) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, s(y0), z6)) F(0, 0, s(0), s(0), 0, 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(y0))) F(0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5, z6) -> c2(F(0, 0, 0, s(s(0)), z1, z2, z3, z4, z5, z6)) F(0, 0, s(0), 0, s(0), s(y0), z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, s(y0), z3, z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, s(y0), z4, z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, s(y0), z5) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, s(0), 0, s(0), 0, 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4, z5) -> c2(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, s(0), 0, 0, s(0), s(y0), z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, s(y0), z3, z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, s(y0), z4) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, s(0), 0, 0, s(0), 0, 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3, z4) -> c2(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, s(0), 0, 0, 0, s(0), s(y0), z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, s(y0), z3) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, s(0), 0, 0, 0, s(0), 0, 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2, z3) -> c2(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, s(0), 0, 0, 0, 0, s(0), s(y0), z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, s(0), 0, 0, 0, 0, s(0), 0, s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1, z2) -> c2(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(0), s(y0)) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, s(s(0)), z1) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, s(0), 0, 0, 0, 0, 0, 0, s(s(0))) -> c2(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6, z7) -> c2(F(s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6, z7)) F(0, 0, 0, s(0), s(0), s(y0), z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), s(y0), z2, z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, s(y0), z3, z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, s(y0), z3, z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, s(y0), z4, z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, s(y0), z4, z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, s(y0), z5) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, s(y0), z5)) F(0, 0, 0, s(0), s(0), 0, 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, s(0), 0, 0, 0, 0, s(y0))) F(0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4, z5) -> c3(F(0, 0, 0, 0, s(s(0)), z1, z2, z3, z4, z5)) F(0, 0, 0, s(0), 0, s(0), s(y0), z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, s(y0), z3, z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, s(y0), z4) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, s(0), 0, s(0), 0, 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3, z4) -> c3(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, s(0), 0, 0, s(0), s(y0), z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, s(y0), z3) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, s(0), 0, 0, s(0), 0, 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, s(0), 0, 0, s(s(s(y0))), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, s(s(0)), z1, z2, z3) -> c3(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) F(0, 0, 0, s(0), 0, 0, 0, s(0), s(y0), z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2)) F(0, 0, 0, s(0), 0, 0, 0, s(0), 0, s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0))) F(0, 0, 0, s(0), 0, 0, 0, s(s(s(y0))), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, s(s(0)), z1, z2) -> c3(F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(0), s(y0)) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0))) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(s(y0))), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1)) F(0, 0, 0, s(0), 0, 0, 0, 0, s(s(0)), z1) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1)) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(s(s(y0)))) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))))) F(0, 0, 0, s(0), 0, 0, 0, 0, 0, s(s(0))) -> c3(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0)))) F(0, 0, 0, s(s(s(s(y0)))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), s(s(s(y0))), z1, z2, z3, z4, z5, z6)) F(0, 0, 0, s(s(s(0))), z1, z2, z3, z4, z5, z6) -> c3(F(s(s(0)), s(s(0)), s(s(0)), s(s(0)), z1, z2, z3, z4, z5, z6)) K tuples: F(0, 0, 0, 0, 0, 0, 0, s(0), s(y0), z2) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, s(y0), z2)) F(0, 0, 0, 0, 0, 0, 0, s(0), 0, s(y0)) -> c7(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2) -> c7(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, s(s(0)), z1, z2) -> c7(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1, z2)) F(0, 0, 0, 0, 0, 0, 0, 0, s(0), s(y0)) -> c8(F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(y0))) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0))), z1) -> c8(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, s(s(0)), z1) -> c8(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), z1)) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(s(y0)))) -> c9(F(s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)), s(s(y0)))) F(0, 0, 0, 0, 0, 0, 0, 0, 0, s(s(0))) -> c9(F(s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0), s(0))) Defined Rule Symbols:none Defined Pair Symbols: F_10 Compound Symbols: c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c8_1, c9_1, c_1, c1_1 ---------------------------------------- (143) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (144) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 [1] Rewrite Strategy: INNERMOST ---------------------------------------- (145) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (146) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 [1] The TRS has the following type information: f :: s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 s :: s:0 -> s:0 0 :: s:0 Rewrite Strategy: INNERMOST ---------------------------------------- (147) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: f_10 (c) The following functions are completely defined: none Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (148) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 [1] The TRS has the following type information: f :: s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 s :: s:0 -> s:0 0 :: s:0 Rewrite Strategy: INNERMOST ---------------------------------------- (149) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (150) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 [1] The TRS has the following type information: f :: s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 s :: s:0 -> s:0 0 :: s:0 Rewrite Strategy: INNERMOST ---------------------------------------- (151) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 ---------------------------------------- (152) Obligation: Complexity RNTS consisting of the following rules: f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) :|: z3 = x6, z' = x2, z7 = x10, x5 >= 0, x8 >= 0, z = 1 + x1, z'' = x3, z2 = x5, x2 >= 0, x3 >= 0, z5 = x8, z1 = x4, x1 >= 0, x4 >= 0, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z7 = 1 + x10, x10 >= 0, z = 0, z6 = 0, z' = 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) :|: z3 = x6, z7 = x10, x5 >= 0, x8 >= 0, z'' = x3, z = 0, z2 = x5, x2 >= 0, x3 >= 0, z5 = x8, z1 = x4, x4 >= 0, z' = 1 + x2, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) :|: z3 = x6, z7 = x10, x5 >= 0, x8 >= 0, z'' = 1 + x3, z = 0, z2 = x5, x3 >= 0, z' = 0, z5 = x8, z1 = x4, x4 >= 0, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) :|: z3 = x6, z7 = x10, x5 >= 0, x8 >= 0, z1 = 1 + x4, z = 0, z2 = x5, z' = 0, z'' = 0, z5 = x8, x4 >= 0, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) :|: z3 = x6, z7 = x10, x5 >= 0, x8 >= 0, z = 0, z' = 0, z'' = 0, z5 = x8, z1 = 0, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, z2 = 1 + x5, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) :|: z3 = 1 + x6, z7 = x10, x8 >= 0, z2 = 0, z = 0, z' = 0, z'' = 0, z5 = x8, z1 = 0, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) :|: z7 = x10, x8 >= 0, z2 = 0, z3 = 0, z = 0, z' = 0, z'' = 0, z5 = x8, z1 = 0, x7 >= 0, z6 = x9, x10 >= 0, x9 >= 0, z4 = 1 + x7 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) :|: z7 = x10, x8 >= 0, z2 = 0, z3 = 0, z = 0, z5 = 1 + x8, z' = 0, z'' = 0, z1 = 0, z4 = 0, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) :|: z'' = 0, z6 = 1 + x9, z1 = 0, z4 = 0, z5 = 0, z7 = x10, z2 = 0, z3 = 0, x10 >= 0, z = 0, x9 >= 0, z' = 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> 0 :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z = 0, z6 = 0, z7 = 0, z' = 0 ---------------------------------------- (153) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (154) Obligation: Complexity RNTS consisting of the following rules: f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z - 1, z', z'', z1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z' >= 0, z'' >= 0, z - 1 >= 0, z1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z' - 1, z' - 1, z'', z1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z = 0, z' - 1 >= 0, z'' >= 0, z1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z'' - 1, z'' - 1, z'' - 1, z1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z = 0, z'' - 1 >= 0, z' = 0, z1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z1 - 1, z1 - 1, z1 - 1, z1 - 1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z = 0, z' = 0, z'' = 0, z1 - 1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z2 - 1, z2 - 1, z2 - 1, z2 - 1, z2 - 1, z3, z4, z5, z6, z7) :|: z2 - 1 >= 0, z5 >= 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z3 - 1, z3 - 1, z3 - 1, z3 - 1, z3 - 1, z3 - 1, z4, z5, z6, z7) :|: z5 >= 0, z2 = 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 >= 0, z3 - 1 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z4 - 1, z4 - 1, z4 - 1, z4 - 1, z4 - 1, z4 - 1, z4 - 1, z5, z6, z7) :|: z5 >= 0, z2 = 0, z3 = 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 - 1 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z6, z7) :|: z5 - 1 >= 0, z2 = 0, z3 = 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 = 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z7) :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z7 >= 0, z = 0, z6 - 1 >= 0, z' = 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1) :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z7 - 1 >= 0, z = 0, z6 = 0, z' = 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> 0 :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z = 0, z6 = 0, z7 = 0, z' = 0 ---------------------------------------- (155) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { f } ---------------------------------------- (156) Obligation: Complexity RNTS consisting of the following rules: f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z - 1, z', z'', z1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z' >= 0, z'' >= 0, z - 1 >= 0, z1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z' - 1, z' - 1, z'', z1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z = 0, z' - 1 >= 0, z'' >= 0, z1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z'' - 1, z'' - 1, z'' - 1, z1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z = 0, z'' - 1 >= 0, z' = 0, z1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z1 - 1, z1 - 1, z1 - 1, z1 - 1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z = 0, z' = 0, z'' = 0, z1 - 1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z2 - 1, z2 - 1, z2 - 1, z2 - 1, z2 - 1, z3, z4, z5, z6, z7) :|: z2 - 1 >= 0, z5 >= 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z3 - 1, z3 - 1, z3 - 1, z3 - 1, z3 - 1, z3 - 1, z4, z5, z6, z7) :|: z5 >= 0, z2 = 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 >= 0, z3 - 1 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z4 - 1, z4 - 1, z4 - 1, z4 - 1, z4 - 1, z4 - 1, z4 - 1, z5, z6, z7) :|: z5 >= 0, z2 = 0, z3 = 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 - 1 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z6, z7) :|: z5 - 1 >= 0, z2 = 0, z3 = 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 = 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z7) :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z7 >= 0, z = 0, z6 - 1 >= 0, z' = 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1) :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z7 - 1 >= 0, z = 0, z6 = 0, z' = 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> 0 :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z = 0, z6 = 0, z7 = 0, z' = 0 Function symbols to be analyzed: {f} ---------------------------------------- (157) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (158) Obligation: Complexity RNTS consisting of the following rules: f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z - 1, z', z'', z1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z' >= 0, z'' >= 0, z - 1 >= 0, z1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z' - 1, z' - 1, z'', z1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z = 0, z' - 1 >= 0, z'' >= 0, z1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z'' - 1, z'' - 1, z'' - 1, z1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z = 0, z'' - 1 >= 0, z' = 0, z1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z1 - 1, z1 - 1, z1 - 1, z1 - 1, z2, z3, z4, z5, z6, z7) :|: z2 >= 0, z5 >= 0, z = 0, z' = 0, z'' = 0, z1 - 1 >= 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z2 - 1, z2 - 1, z2 - 1, z2 - 1, z2 - 1, z3, z4, z5, z6, z7) :|: z2 - 1 >= 0, z5 >= 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 >= 0, z3 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z3 - 1, z3 - 1, z3 - 1, z3 - 1, z3 - 1, z3 - 1, z4, z5, z6, z7) :|: z5 >= 0, z2 = 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 >= 0, z3 - 1 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z4 - 1, z4 - 1, z4 - 1, z4 - 1, z4 - 1, z4 - 1, z4 - 1, z5, z6, z7) :|: z5 >= 0, z2 = 0, z3 = 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 - 1 >= 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z5 - 1, z6, z7) :|: z5 - 1 >= 0, z2 = 0, z3 = 0, z = 0, z' = 0, z'' = 0, z1 = 0, z4 = 0, z7 >= 0, z6 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z6 - 1, z7) :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z7 >= 0, z = 0, z6 - 1 >= 0, z' = 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1, z7 - 1) :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z7 - 1 >= 0, z = 0, z6 = 0, z' = 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> 0 :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z = 0, z6 = 0, z7 = 0, z' = 0 Function symbols to be analyzed: {f} ---------------------------------------- (159) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: none And the following fresh constants: none ---------------------------------------- (160) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: f(s(x1), x2, x3, x4, x5, x6, x7, x8, x9, x10) -> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, s(x2), x3, x4, x5, x6, x7, x8, x9, x10) -> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, s(x3), x4, x5, x6, x7, x8, x9, x10) -> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, s(x4), x5, x6, x7, x8, x9, x10) -> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, s(x5), x6, x7, x8, x9, x10) -> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, s(x6), x7, x8, x9, x10) -> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, s(x7), x8, x9, x10) -> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, s(x8), x9, x10) -> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, s(x9), x10) -> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, 0, s(x10)) -> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) [1] f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 0 [1] The TRS has the following type information: f :: s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 -> s:0 s :: s:0 -> s:0 0 :: s:0 Rewrite Strategy: INNERMOST ---------------------------------------- (161) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 ---------------------------------------- (162) Obligation: Complexity RNTS consisting of the following rules: f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) :|: z3 = x6, z' = x2, z7 = x10, x5 >= 0, x8 >= 0, z = 1 + x1, z'' = x3, z2 = x5, x2 >= 0, x3 >= 0, z5 = x8, z1 = x4, x1 >= 0, x4 >= 0, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x10, x10, x10, x10, x10, x10, x10, x10, x10, x10) :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z7 = 1 + x10, x10 >= 0, z = 0, z6 = 0, z' = 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x2, x2, x3, x4, x5, x6, x7, x8, x9, x10) :|: z3 = x6, z7 = x10, x5 >= 0, x8 >= 0, z'' = x3, z = 0, z2 = x5, x2 >= 0, x3 >= 0, z5 = x8, z1 = x4, x4 >= 0, z' = 1 + x2, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x3, x3, x3, x4, x5, x6, x7, x8, x9, x10) :|: z3 = x6, z7 = x10, x5 >= 0, x8 >= 0, z'' = 1 + x3, z = 0, z2 = x5, x3 >= 0, z' = 0, z5 = x8, z1 = x4, x4 >= 0, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x4, x4, x4, x4, x5, x6, x7, x8, x9, x10) :|: z3 = x6, z7 = x10, x5 >= 0, x8 >= 0, z1 = 1 + x4, z = 0, z2 = x5, z' = 0, z'' = 0, z5 = x8, x4 >= 0, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x5, x5, x5, x5, x5, x6, x7, x8, x9, x10) :|: z3 = x6, z7 = x10, x5 >= 0, x8 >= 0, z = 0, z' = 0, z'' = 0, z5 = x8, z1 = 0, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, z2 = 1 + x5, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x6, x6, x6, x6, x6, x6, x7, x8, x9, x10) :|: z3 = 1 + x6, z7 = x10, x8 >= 0, z2 = 0, z = 0, z' = 0, z'' = 0, z5 = x8, z1 = 0, x7 >= 0, x6 >= 0, z4 = x7, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x7, x7, x7, x7, x7, x7, x7, x8, x9, x10) :|: z7 = x10, x8 >= 0, z2 = 0, z3 = 0, z = 0, z' = 0, z'' = 0, z5 = x8, z1 = 0, x7 >= 0, z6 = x9, x10 >= 0, x9 >= 0, z4 = 1 + x7 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x8, x8, x8, x8, x8, x8, x8, x8, x9, x10) :|: z7 = x10, x8 >= 0, z2 = 0, z3 = 0, z = 0, z5 = 1 + x8, z' = 0, z'' = 0, z1 = 0, z4 = 0, z6 = x9, x10 >= 0, x9 >= 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> f(x9, x9, x9, x9, x9, x9, x9, x9, x9, x10) :|: z'' = 0, z6 = 1 + x9, z1 = 0, z4 = 0, z5 = 0, z7 = x10, z2 = 0, z3 = 0, x10 >= 0, z = 0, x9 >= 0, z' = 0 f(z, z', z'', z1, z2, z3, z4, z5, z6, z7) -{ 1 }-> 0 :|: z'' = 0, z1 = 0, z4 = 0, z5 = 0, z2 = 0, z3 = 0, z = 0, z6 = 0, z7 = 0, z' = 0 Only complete derivations are relevant for the runtime complexity.