KILLED proof of input_0AMcgN5sZu.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 16 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 30 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) CompletionProof [UPPER BOUND(ID), 0 ms] (22) CpxTypedWeightedCompleteTrs (23) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (26) CdtProblem (27) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 133 ms] (32) CdtProblem (33) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 243 ms] (34) CdtProblem (35) CdtRuleRemovalProof [UPPER BOUND(ADD(n^3)), 1048 ms] (36) CdtProblem (37) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2 ms] (38) CdtProblem (39) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 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), 1 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), 2 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 ---------------------------------------- (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) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) 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 ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) 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 ---------------------------------------- (9) 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 ---------------------------------------- (10) 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 ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) 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 ---------------------------------------- (13) 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 ---------------------------------------- (14) 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 ---------------------------------------- (15) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (16) 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 ---------------------------------------- (17) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { f } ---------------------------------------- (18) 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} ---------------------------------------- (19) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (20) 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} ---------------------------------------- (21) 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 ---------------------------------------- (22) 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 ---------------------------------------- (23) 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 ---------------------------------------- (24) 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. ---------------------------------------- (25) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (26) 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 ---------------------------------------- (27) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: F(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> c10 ---------------------------------------- (28) 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 ---------------------------------------- (29) 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 ---------------------------------------- (30) 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 ---------------------------------------- (31) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) 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) = [1] POL(F(x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_10)) = x_10 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 ---------------------------------------- (32) 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 ---------------------------------------- (33) 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 ---------------------------------------- (34) 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 ---------------------------------------- (35) 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 ---------------------------------------- (36) 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 ---------------------------------------- (37) 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))) ---------------------------------------- (38) 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 ---------------------------------------- (39) 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)) ---------------------------------------- (40) 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 ---------------------------------------- (41) 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)) ---------------------------------------- (42) 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 ---------------------------------------- (43) 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)) ---------------------------------------- (44) 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 ---------------------------------------- (45) 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)) ---------------------------------------- (46) 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 ---------------------------------------- (47) 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)) ---------------------------------------- (48) 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 ---------------------------------------- (49) 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)) ---------------------------------------- (50) 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 ---------------------------------------- (51) 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)) ---------------------------------------- (52) 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 ---------------------------------------- (53) 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)) ---------------------------------------- (54) 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 ---------------------------------------- (55) 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))) ---------------------------------------- (56) 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 ---------------------------------------- (57) 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))) ---------------------------------------- (58) 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 ---------------------------------------- (59) 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)) ---------------------------------------- (60) 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 ---------------------------------------- (61) 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)) ---------------------------------------- (62) 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 ---------------------------------------- (63) 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)) ---------------------------------------- (64) 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 ---------------------------------------- (65) 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)) ---------------------------------------- (66) 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 ---------------------------------------- (67) 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)) ---------------------------------------- (68) 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 ---------------------------------------- (69) 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)) ---------------------------------------- (70) 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 ---------------------------------------- (71) 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)) ---------------------------------------- (72) 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 ---------------------------------------- (73) 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)) ---------------------------------------- (74) 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 ---------------------------------------- (75) 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)))) ---------------------------------------- (76) 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 ---------------------------------------- (77) 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)) ---------------------------------------- (78) 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 ---------------------------------------- (79) 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)) ---------------------------------------- (80) 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 ---------------------------------------- (81) 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)) ---------------------------------------- (82) 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 ---------------------------------------- (83) 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)) ---------------------------------------- (84) 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 ---------------------------------------- (85) 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)) ---------------------------------------- (86) 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 ---------------------------------------- (87) 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)) ---------------------------------------- (88) 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 ---------------------------------------- (89) 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)) ---------------------------------------- (90) 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 ---------------------------------------- (91) 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)))) ---------------------------------------- (92) 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 ---------------------------------------- (93) 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)) ---------------------------------------- (94) 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 ---------------------------------------- (95) 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))) ---------------------------------------- (96) 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 ---------------------------------------- (97) 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)) ---------------------------------------- (98) 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 ---------------------------------------- (99) 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)) ---------------------------------------- (100) 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 ---------------------------------------- (101) 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)) ---------------------------------------- (102) 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 ---------------------------------------- (103) 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)) ---------------------------------------- (104) 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 ---------------------------------------- (105) 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)) ---------------------------------------- (106) 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 ---------------------------------------- (107) 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)) ---------------------------------------- (108) 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 ---------------------------------------- (109) 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)))) ---------------------------------------- (110) 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 ---------------------------------------- (111) 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)) ---------------------------------------- (112) 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 ---------------------------------------- (113) 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)) ---------------------------------------- (114) 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 ---------------------------------------- (115) 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)) ---------------------------------------- (116) 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 ---------------------------------------- (117) 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)) ---------------------------------------- (118) 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 ---------------------------------------- (119) 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)) ---------------------------------------- (120) 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 ---------------------------------------- (121) 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)) ---------------------------------------- (122) 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 ---------------------------------------- (123) 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)))) ---------------------------------------- (124) 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 ---------------------------------------- (125) 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)) ---------------------------------------- (126) 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 ---------------------------------------- (127) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace 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)) by F(0, 0, 0, 0, s(0), s(0), s(y0), z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, 0, s(0), s(0), 0, s(y0), z3, z4) -> c4(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, 0, s(0), s(0), 0, 0, s(y0), z4) -> c4(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, 0, s(0), s(0), 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) ---------------------------------------- (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(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), 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)) F(0, 0, 0, 0, s(0), s(0), s(y0), z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, 0, s(0), s(0), 0, s(y0), z3, z4) -> c4(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, 0, s(0), s(0), 0, 0, s(y0), z4) -> c4(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, 0, s(0), s(0), 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4) -> c4(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(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), 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)) F(0, 0, 0, 0, s(0), s(0), s(y0), z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, 0, s(0), s(0), 0, s(y0), z3, z4) -> c4(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, 0, s(0), s(0), 0, 0, s(y0), z4) -> c4(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, 0, s(0), s(0), 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4) -> c4(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 ---------------------------------------- (129) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace 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)) by F(0, 0, 0, 0, s(0), 0, s(0), s(y0), z2, z3) -> c4(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, 0, s(0), 0, s(0), 0, s(y0), z3) -> c4(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, 0, s(0), 0, s(0), 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3) -> c4(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3) -> c4(F(0, 0, 0, 0, 0, 0, s(s(0)), z1, z2, z3)) ---------------------------------------- (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(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), 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)) F(0, 0, 0, 0, s(0), s(0), s(y0), z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, 0, s(0), s(0), 0, s(y0), z3, z4) -> c4(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, 0, s(0), s(0), 0, 0, s(y0), z4) -> c4(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, 0, s(0), s(0), 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, 0, s(0), 0, s(0), s(y0), z2, z3) -> c4(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, 0, s(0), 0, s(0), 0, s(y0), z3) -> c4(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, 0, s(0), 0, s(0), 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3) -> c4(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3) -> c4(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(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), 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)) F(0, 0, 0, 0, s(0), s(0), s(y0), z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(0), s(y0), z2, z3, z4)) F(0, 0, 0, 0, s(0), s(0), 0, s(y0), z3, z4) -> c4(F(0, 0, 0, 0, 0, s(0), 0, s(y0), z3, z4)) F(0, 0, 0, 0, s(0), s(0), 0, 0, s(y0), z4) -> c4(F(0, 0, 0, 0, 0, s(0), 0, 0, s(y0), z4)) F(0, 0, 0, 0, s(0), s(0), 0, 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, s(0), 0, 0, 0, s(y0))) F(0, 0, 0, 0, s(0), s(s(s(y0))), z1, z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3, z4)) F(0, 0, 0, 0, s(0), s(s(0)), z1, z2, z3, z4) -> c4(F(0, 0, 0, 0, 0, s(s(0)), z1, z2, z3, z4)) F(0, 0, 0, 0, s(0), 0, s(0), s(y0), z2, z3) -> c4(F(0, 0, 0, 0, 0, 0, s(0), s(y0), z2, z3)) F(0, 0, 0, 0, s(0), 0, s(0), 0, s(y0), z3) -> c4(F(0, 0, 0, 0, 0, 0, s(0), 0, s(y0), z3)) F(0, 0, 0, 0, s(0), 0, s(0), 0, 0, s(y0)) -> c4(F(0, 0, 0, 0, 0, 0, s(0), 0, 0, s(y0))) F(0, 0, 0, 0, s(0), 0, s(s(s(y0))), z1, z2, z3) -> c4(F(0, 0, 0, 0, 0, 0, s(s(s(y0))), z1, z2, z3)) F(0, 0, 0, 0, s(0), 0, s(s(0)), z1, z2, z3) -> c4(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