KILLED proof of input_DAnWjNlwXS.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 9 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 289 ms] (16) typed CpxTrs (17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (18) TRS for Loop Detection (19) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (20) CpxWeightedTrs (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxTypedWeightedTrs (23) CompletionProof [UPPER BOUND(ID), 0 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) CompletionProof [UPPER BOUND(ID), 0 ms] (28) CpxTypedWeightedCompleteTrs (29) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) InliningProof [UPPER BOUND(ID), 1015 ms] (34) CpxRNTS (35) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CpxRNTS (37) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (38) CdtProblem (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CpxRelTRS (43) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (44) CpxTRS (45) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CpxWeightedTrs (47) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CpxTypedWeightedTrs (49) CompletionProof [UPPER BOUND(ID), 0 ms] (50) CpxTypedWeightedCompleteTrs (51) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CpxTypedWeightedCompleteTrs (53) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (54) CpxRNTS (55) InliningProof [UPPER BOUND(ID), 814 ms] (56) CpxRNTS (57) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CpxRNTS (59) CompletionProof [UPPER BOUND(ID), 0 ms] (60) CpxTypedWeightedCompleteTrs (61) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (62) CpxRNTS (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 392 ms] (148) CdtProblem (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 791 ms] (152) CdtProblem (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1662 ms] (156) CdtProblem (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1648 ms] (160) CdtProblem (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 42 ms] (164) CdtProblem (165) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 13 ms] (166) CdtProblem (167) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 23 ms] (168) CdtProblem (169) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 54 ms] (170) CdtProblem (171) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 81 ms] (172) CdtProblem (173) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 195 ms] (174) CdtProblem (175) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 627 ms] (176) CdtProblem (177) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1994 ms] (178) CdtProblem (179) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 7364 ms] (180) 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: a__f(a, b, X) -> a__f(mark(X), X, mark(X)) a__c -> a a__c -> b mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) mark(c) -> a__c mark(a) -> a mark(b) -> b a__f(X1, X2, X3) -> f(X1, X2, X3) a__c -> c 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: a__f(a, b, X) -> a__f(mark(X), X, mark(X)) a__c -> a a__c -> b mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) mark(c) -> a__c mark(a) -> a mark(b) -> b a__f(X1, X2, X3) -> f(X1, X2, X3) a__c -> c 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: a__f(a, b, X) -> a__f(mark(X), X, mark(X)) a__c -> a a__c -> b mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) mark(c) -> a__c mark(a) -> a mark(b) -> b a__f(X1, X2, X3) -> f(X1, X2, X3) a__c -> c S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(z0, z1, z2) -> c3 A__C -> c4 A__C -> c5 A__C -> c6 MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) MARK(c) -> c9(A__C) MARK(a) -> c10 MARK(b) -> c11 S tuples: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(z0, z1, z2) -> c3 A__C -> c4 A__C -> c5 A__C -> c6 MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) MARK(c) -> c9(A__C) MARK(a) -> c10 MARK(b) -> c11 K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, A__C, MARK_1 Compound Symbols: c1_2, c2_2, c3, c4, c5, c6, c7_2, c8_2, c9_1, c10, c11 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(z0, z1, z2) -> c3 A__C -> c4 A__C -> c5 A__C -> c6 MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) MARK(c) -> c9(A__C) MARK(a) -> c10 MARK(b) -> c11 The (relative) TRS S consists of the following rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(z0, z1, z2) -> c3 A__C -> c4 A__C -> c5 A__C -> c6 MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) MARK(c) -> c9(A__C) MARK(a) -> c10 MARK(b) -> c11 The (relative) TRS S consists of the following rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(z0, z1, z2) -> c3 A__C -> c4 A__C -> c5 A__C -> c6 MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) MARK(c) -> c9(A__C) MARK(a) -> c10 MARK(b) -> c11 a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Types: A__F :: a:b:f:c -> a:b:f:c -> a:b:f:c -> c1:c2:c3 a :: a:b:f:c b :: a:b:f:c c1 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c1:c2:c3 mark :: a:b:f:c -> a:b:f:c MARK :: a:b:f:c -> c7:c8:c9:c10:c11 c2 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c1:c2:c3 c3 :: c1:c2:c3 A__C :: c4:c5:c6 c4 :: c4:c5:c6 c5 :: c4:c5:c6 c6 :: c4:c5:c6 f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c c7 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c7:c8:c9:c10:c11 c8 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c7:c8:c9:c10:c11 c :: a:b:f:c c9 :: c4:c5:c6 -> c7:c8:c9:c10:c11 c10 :: c7:c8:c9:c10:c11 c11 :: c7:c8:c9:c10:c11 a__f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c a__c :: a:b:f:c hole_c1:c2:c31_12 :: c1:c2:c3 hole_a:b:f:c2_12 :: a:b:f:c hole_c7:c8:c9:c10:c113_12 :: c7:c8:c9:c10:c11 hole_c4:c5:c64_12 :: c4:c5:c6 gen_c1:c2:c35_12 :: Nat -> c1:c2:c3 gen_a:b:f:c6_12 :: Nat -> a:b:f:c gen_c7:c8:c9:c10:c117_12 :: Nat -> c7:c8:c9:c10:c11 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__F, mark, MARK, a__f They will be analysed ascendingly in the following order: mark < A__F A__F = MARK mark < MARK mark = a__f ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(z0, z1, z2) -> c3 A__C -> c4 A__C -> c5 A__C -> c6 MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) MARK(c) -> c9(A__C) MARK(a) -> c10 MARK(b) -> c11 a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Types: A__F :: a:b:f:c -> a:b:f:c -> a:b:f:c -> c1:c2:c3 a :: a:b:f:c b :: a:b:f:c c1 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c1:c2:c3 mark :: a:b:f:c -> a:b:f:c MARK :: a:b:f:c -> c7:c8:c9:c10:c11 c2 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c1:c2:c3 c3 :: c1:c2:c3 A__C :: c4:c5:c6 c4 :: c4:c5:c6 c5 :: c4:c5:c6 c6 :: c4:c5:c6 f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c c7 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c7:c8:c9:c10:c11 c8 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c7:c8:c9:c10:c11 c :: a:b:f:c c9 :: c4:c5:c6 -> c7:c8:c9:c10:c11 c10 :: c7:c8:c9:c10:c11 c11 :: c7:c8:c9:c10:c11 a__f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c a__c :: a:b:f:c hole_c1:c2:c31_12 :: c1:c2:c3 hole_a:b:f:c2_12 :: a:b:f:c hole_c7:c8:c9:c10:c113_12 :: c7:c8:c9:c10:c11 hole_c4:c5:c64_12 :: c4:c5:c6 gen_c1:c2:c35_12 :: Nat -> c1:c2:c3 gen_a:b:f:c6_12 :: Nat -> a:b:f:c gen_c7:c8:c9:c10:c117_12 :: Nat -> c7:c8:c9:c10:c11 Generator Equations: gen_c1:c2:c35_12(0) <=> c3 gen_c1:c2:c35_12(+(x, 1)) <=> c1(gen_c1:c2:c35_12(x), c9(c4)) gen_a:b:f:c6_12(0) <=> a gen_a:b:f:c6_12(+(x, 1)) <=> f(a, a, gen_a:b:f:c6_12(x)) gen_c7:c8:c9:c10:c117_12(0) <=> c9(c4) gen_c7:c8:c9:c10:c117_12(+(x, 1)) <=> c7(c3, gen_c7:c8:c9:c10:c117_12(x)) The following defined symbols remain to be analysed: a__f, A__F, mark, MARK They will be analysed ascendingly in the following order: mark < A__F A__F = MARK mark < MARK mark = a__f ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_a:b:f:c6_12(n20_12)) -> gen_a:b:f:c6_12(n20_12), rt in Omega(0) Induction Base: mark(gen_a:b:f:c6_12(0)) ->_R^Omega(0) a Induction Step: mark(gen_a:b:f:c6_12(+(n20_12, 1))) ->_R^Omega(0) a__f(mark(a), a, mark(gen_a:b:f:c6_12(n20_12))) ->_R^Omega(0) a__f(a, a, mark(gen_a:b:f:c6_12(n20_12))) ->_IH a__f(a, a, gen_a:b:f:c6_12(c21_12)) ->_R^Omega(0) f(a, a, gen_a:b:f:c6_12(n20_12)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(z0, z1, z2) -> c3 A__C -> c4 A__C -> c5 A__C -> c6 MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) MARK(c) -> c9(A__C) MARK(a) -> c10 MARK(b) -> c11 a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Types: A__F :: a:b:f:c -> a:b:f:c -> a:b:f:c -> c1:c2:c3 a :: a:b:f:c b :: a:b:f:c c1 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c1:c2:c3 mark :: a:b:f:c -> a:b:f:c MARK :: a:b:f:c -> c7:c8:c9:c10:c11 c2 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c1:c2:c3 c3 :: c1:c2:c3 A__C :: c4:c5:c6 c4 :: c4:c5:c6 c5 :: c4:c5:c6 c6 :: c4:c5:c6 f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c c7 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c7:c8:c9:c10:c11 c8 :: c1:c2:c3 -> c7:c8:c9:c10:c11 -> c7:c8:c9:c10:c11 c :: a:b:f:c c9 :: c4:c5:c6 -> c7:c8:c9:c10:c11 c10 :: c7:c8:c9:c10:c11 c11 :: c7:c8:c9:c10:c11 a__f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c a__c :: a:b:f:c hole_c1:c2:c31_12 :: c1:c2:c3 hole_a:b:f:c2_12 :: a:b:f:c hole_c7:c8:c9:c10:c113_12 :: c7:c8:c9:c10:c11 hole_c4:c5:c64_12 :: c4:c5:c6 gen_c1:c2:c35_12 :: Nat -> c1:c2:c3 gen_a:b:f:c6_12 :: Nat -> a:b:f:c gen_c7:c8:c9:c10:c117_12 :: Nat -> c7:c8:c9:c10:c11 Lemmas: mark(gen_a:b:f:c6_12(n20_12)) -> gen_a:b:f:c6_12(n20_12), rt in Omega(0) Generator Equations: gen_c1:c2:c35_12(0) <=> c3 gen_c1:c2:c35_12(+(x, 1)) <=> c1(gen_c1:c2:c35_12(x), c9(c4)) gen_a:b:f:c6_12(0) <=> a gen_a:b:f:c6_12(+(x, 1)) <=> f(a, a, gen_a:b:f:c6_12(x)) gen_c7:c8:c9:c10:c117_12(0) <=> c9(c4) gen_c7:c8:c9:c10:c117_12(+(x, 1)) <=> c7(c3, gen_c7:c8:c9:c10:c117_12(x)) The following defined symbols remain to be analysed: a__f, A__F, MARK They will be analysed ascendingly in the following order: mark < A__F A__F = MARK mark < MARK mark = a__f ---------------------------------------- (17) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (18) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(z0, z1, z2) -> c3 A__C -> c4 A__C -> c5 A__C -> c6 MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) MARK(c) -> c9(A__C) MARK(a) -> c10 MARK(b) -> c11 The (relative) TRS S consists of the following rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Rewrite Strategy: INNERMOST ---------------------------------------- (19) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (20) 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: a__f(a, b, X) -> a__f(mark(X), X, mark(X)) [1] a__c -> a [1] a__c -> b [1] mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) [1] mark(c) -> a__c [1] mark(a) -> a [1] mark(b) -> b [1] a__f(X1, X2, X3) -> f(X1, X2, X3) [1] a__c -> c [1] Rewrite Strategy: INNERMOST ---------------------------------------- (21) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__f(a, b, X) -> a__f(mark(X), X, mark(X)) [1] a__c -> a [1] a__c -> b [1] mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) [1] mark(c) -> a__c [1] mark(a) -> a [1] mark(b) -> b [1] a__f(X1, X2, X3) -> f(X1, X2, X3) [1] a__c -> c [1] The TRS has the following type information: a__f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c a :: a:b:f:c b :: a:b:f:c mark :: a:b:f:c -> a:b:f:c a__c :: a:b:f:c f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c c :: a:b:f:c Rewrite Strategy: INNERMOST ---------------------------------------- (23) 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 ---------------------------------------- (24) 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: a__f(a, b, X) -> a__f(mark(X), X, mark(X)) [1] a__c -> a [1] a__c -> b [1] mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) [1] mark(c) -> a__c [1] mark(a) -> a [1] mark(b) -> b [1] a__f(X1, X2, X3) -> f(X1, X2, X3) [1] a__c -> c [1] The TRS has the following type information: a__f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c a :: a:b:f:c b :: a:b:f:c mark :: a:b:f:c -> a:b:f:c a__c :: a:b:f:c f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c c :: a:b:f:c Rewrite Strategy: INNERMOST ---------------------------------------- (25) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: a => 0 b => 1 c => 2 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: a__c -{ 1 }-> 2 :|: a__c -{ 1 }-> 1 :|: a__c -{ 1 }-> 0 :|: a__f(z, z', z'') -{ 1 }-> a__f(mark(X), X, mark(X)) :|: z'' = X, X >= 0, z' = 1, z = 0 a__f(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 mark(z) -{ 1 }-> a__f(mark(X1), X2, mark(X3)) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__c :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (27) 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: none (c) The following functions are completely defined: mark_1 a__c a__f_3 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (28) 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: a__f(a, b, X) -> a__f(mark(X), X, mark(X)) [1] a__c -> a [1] a__c -> b [1] mark(f(X1, X2, X3)) -> a__f(mark(X1), X2, mark(X3)) [1] mark(c) -> a__c [1] mark(a) -> a [1] mark(b) -> b [1] a__f(X1, X2, X3) -> f(X1, X2, X3) [1] a__c -> c [1] The TRS has the following type information: a__f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c a :: a:b:f:c b :: a:b:f:c mark :: a:b:f:c -> a:b:f:c a__c :: a:b:f:c f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c c :: a:b:f:c Rewrite Strategy: INNERMOST ---------------------------------------- (29) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (30) 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: a__f(a, b, f(X1', X2', X3')) -> a__f(a__f(mark(X1'), X2', mark(X3')), f(X1', X2', X3'), a__f(mark(X1'), X2', mark(X3'))) [3] a__f(a, b, c) -> a__f(a__c, c, a__c) [3] a__f(a, b, a) -> a__f(a, a, a) [3] a__f(a, b, b) -> a__f(b, b, b) [3] a__c -> a [1] a__c -> b [1] mark(f(f(X1'', X2'', X3''), X2, f(X11, X21, X31))) -> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, a__f(mark(X11), X21, mark(X31))) [3] mark(f(f(X1'', X2'', X3''), X2, c)) -> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, a__c) [3] mark(f(f(X1'', X2'', X3''), X2, a)) -> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, a) [3] mark(f(f(X1'', X2'', X3''), X2, b)) -> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, b) [3] mark(f(c, X2, f(X12, X22, X32))) -> a__f(a__c, X2, a__f(mark(X12), X22, mark(X32))) [3] mark(f(c, X2, c)) -> a__f(a__c, X2, a__c) [3] mark(f(c, X2, a)) -> a__f(a__c, X2, a) [3] mark(f(c, X2, b)) -> a__f(a__c, X2, b) [3] mark(f(a, X2, f(X13, X23, X33))) -> a__f(a, X2, a__f(mark(X13), X23, mark(X33))) [3] mark(f(a, X2, c)) -> a__f(a, X2, a__c) [3] mark(f(a, X2, a)) -> a__f(a, X2, a) [3] mark(f(a, X2, b)) -> a__f(a, X2, b) [3] mark(f(b, X2, f(X14, X24, X34))) -> a__f(b, X2, a__f(mark(X14), X24, mark(X34))) [3] mark(f(b, X2, c)) -> a__f(b, X2, a__c) [3] mark(f(b, X2, a)) -> a__f(b, X2, a) [3] mark(f(b, X2, b)) -> a__f(b, X2, b) [3] mark(c) -> a__c [1] mark(a) -> a [1] mark(b) -> b [1] a__f(X1, X2, X3) -> f(X1, X2, X3) [1] a__c -> c [1] The TRS has the following type information: a__f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c a :: a:b:f:c b :: a:b:f:c mark :: a:b:f:c -> a:b:f:c a__c :: a:b:f:c f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c c :: a:b:f:c Rewrite Strategy: INNERMOST ---------------------------------------- (31) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: a => 0 b => 1 c => 2 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: a__c -{ 1 }-> 2 :|: a__c -{ 1 }-> 1 :|: a__c -{ 1 }-> 0 :|: a__f(z, z', z'') -{ 3 }-> a__f(a__f(mark(X1'), X2', mark(X3')), 1 + X1' + X2' + X3', a__f(mark(X1'), X2', mark(X3'))) :|: X3' >= 0, X2' >= 0, X1' >= 0, z'' = 1 + X1' + X2' + X3', z' = 1, z = 0 a__f(z, z', z'') -{ 3 }-> a__f(a__c, 2, a__c) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 3 }-> a__f(1, 1, 1) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 3 }-> a__f(0, 0, 0) :|: z'' = 0, z' = 1, z = 0 a__f(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 mark(z) -{ 3 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, a__f(mark(X11), X21, mark(X31))) :|: X1'' >= 0, X11 >= 0, X21 >= 0, X3'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + (1 + X11 + X21 + X31), X31 >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, a__c) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 2, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 1) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 1, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 0) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 0, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(a__c, X2, a__f(mark(X12), X22, mark(X32))) :|: z = 1 + 2 + X2 + (1 + X12 + X22 + X32), X12 >= 0, X22 >= 0, X32 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(a__c, X2, a__c) :|: z = 1 + 2 + X2 + 2, X2 >= 0 mark(z) -{ 3 }-> a__f(a__c, X2, 1) :|: z = 1 + 2 + X2 + 1, X2 >= 0 mark(z) -{ 3 }-> a__f(a__c, X2, 0) :|: z = 1 + 2 + X2 + 0, X2 >= 0 mark(z) -{ 3 }-> a__f(1, X2, a__f(mark(X14), X24, mark(X34))) :|: z = 1 + 1 + X2 + (1 + X14 + X24 + X34), X2 >= 0, X14 >= 0, X24 >= 0, X34 >= 0 mark(z) -{ 3 }-> a__f(1, X2, a__c) :|: X2 >= 0, z = 1 + 1 + X2 + 2 mark(z) -{ 3 }-> a__f(1, X2, 1) :|: z = 1 + 1 + X2 + 1, X2 >= 0 mark(z) -{ 3 }-> a__f(1, X2, 0) :|: z = 1 + 1 + X2 + 0, X2 >= 0 mark(z) -{ 3 }-> a__f(0, X2, a__f(mark(X13), X23, mark(X33))) :|: X33 >= 0, X2 >= 0, z = 1 + 0 + X2 + (1 + X13 + X23 + X33), X13 >= 0, X23 >= 0 mark(z) -{ 3 }-> a__f(0, X2, a__c) :|: X2 >= 0, z = 1 + 0 + X2 + 2 mark(z) -{ 3 }-> a__f(0, X2, 1) :|: X2 >= 0, z = 1 + 0 + X2 + 1 mark(z) -{ 3 }-> a__f(0, X2, 0) :|: X2 >= 0, z = 1 + 0 + X2 + 0 mark(z) -{ 1 }-> a__c :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 ---------------------------------------- (33) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__c -{ 1 }-> 0 :|: a__c -{ 1 }-> 1 :|: a__c -{ 1 }-> 2 :|: ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: a__c -{ 1 }-> 2 :|: a__c -{ 1 }-> 1 :|: a__c -{ 1 }-> 0 :|: a__f(z, z', z'') -{ 3 }-> a__f(a__f(mark(X1'), X2', mark(X3')), 1 + X1' + X2' + X3', a__f(mark(X1'), X2', mark(X3'))) :|: X3' >= 0, X2' >= 0, X1' >= 0, z'' = 1 + X1' + X2' + X3', z' = 1, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(2, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(2, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(2, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(1, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(1, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(1, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 3 }-> a__f(1, 1, 1) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 5 }-> a__f(0, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(0, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(0, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 3 }-> a__f(0, 0, 0) :|: z'' = 0, z' = 1, z = 0 a__f(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 mark(z) -{ 3 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, a__f(mark(X11), X21, mark(X31))) :|: X1'' >= 0, X11 >= 0, X21 >= 0, X3'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + (1 + X11 + X21 + X31), X31 >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 4 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 2) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 2, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 1) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 1, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 4 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 1) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 2, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 0) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 0, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 4 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 0) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 2, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 4 }-> a__f(2, X2, a__f(mark(X12), X22, mark(X32))) :|: z = 1 + 2 + X2 + (1 + X12 + X22 + X32), X12 >= 0, X22 >= 0, X32 >= 0, X2 >= 0 mark(z) -{ 5 }-> a__f(2, X2, 2) :|: z = 1 + 2 + X2 + 2, X2 >= 0 mark(z) -{ 5 }-> a__f(2, X2, 1) :|: z = 1 + 2 + X2 + 2, X2 >= 0 mark(z) -{ 4 }-> a__f(2, X2, 1) :|: z = 1 + 2 + X2 + 1, X2 >= 0 mark(z) -{ 5 }-> a__f(2, X2, 0) :|: z = 1 + 2 + X2 + 2, X2 >= 0 mark(z) -{ 4 }-> a__f(2, X2, 0) :|: z = 1 + 2 + X2 + 0, X2 >= 0 mark(z) -{ 4 }-> a__f(1, X2, a__f(mark(X12), X22, mark(X32))) :|: z = 1 + 2 + X2 + (1 + X12 + X22 + X32), X12 >= 0, X22 >= 0, X32 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(1, X2, a__f(mark(X14), X24, mark(X34))) :|: z = 1 + 1 + X2 + (1 + X14 + X24 + X34), X2 >= 0, X14 >= 0, X24 >= 0, X34 >= 0 mark(z) -{ 5 }-> a__f(1, X2, 2) :|: z = 1 + 2 + X2 + 2, X2 >= 0 mark(z) -{ 4 }-> a__f(1, X2, 2) :|: X2 >= 0, z = 1 + 1 + X2 + 2 mark(z) -{ 3 }-> a__f(1, X2, 1) :|: z = 1 + 1 + X2 + 1, X2 >= 0 mark(z) -{ 5 }-> a__f(1, X2, 1) :|: z = 1 + 2 + X2 + 2, X2 >= 0 mark(z) -{ 4 }-> a__f(1, X2, 1) :|: z = 1 + 2 + X2 + 1, X2 >= 0 mark(z) -{ 4 }-> a__f(1, X2, 1) :|: X2 >= 0, z = 1 + 1 + X2 + 2 mark(z) -{ 3 }-> a__f(1, X2, 0) :|: z = 1 + 1 + X2 + 0, X2 >= 0 mark(z) -{ 5 }-> a__f(1, X2, 0) :|: z = 1 + 2 + X2 + 2, X2 >= 0 mark(z) -{ 4 }-> a__f(1, X2, 0) :|: z = 1 + 2 + X2 + 0, X2 >= 0 mark(z) -{ 4 }-> a__f(1, X2, 0) :|: X2 >= 0, z = 1 + 1 + X2 + 2 mark(z) -{ 4 }-> a__f(0, X2, a__f(mark(X12), X22, mark(X32))) :|: z = 1 + 2 + X2 + (1 + X12 + X22 + X32), X12 >= 0, X22 >= 0, X32 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(0, X2, a__f(mark(X13), X23, mark(X33))) :|: X33 >= 0, X2 >= 0, z = 1 + 0 + X2 + (1 + X13 + X23 + X33), X13 >= 0, X23 >= 0 mark(z) -{ 5 }-> a__f(0, X2, 2) :|: z = 1 + 2 + X2 + 2, X2 >= 0 mark(z) -{ 4 }-> a__f(0, X2, 2) :|: X2 >= 0, z = 1 + 0 + X2 + 2 mark(z) -{ 3 }-> a__f(0, X2, 1) :|: X2 >= 0, z = 1 + 0 + X2 + 1 mark(z) -{ 5 }-> a__f(0, X2, 1) :|: z = 1 + 2 + X2 + 2, X2 >= 0 mark(z) -{ 4 }-> a__f(0, X2, 1) :|: z = 1 + 2 + X2 + 1, X2 >= 0 mark(z) -{ 4 }-> a__f(0, X2, 1) :|: X2 >= 0, z = 1 + 0 + X2 + 2 mark(z) -{ 3 }-> a__f(0, X2, 0) :|: X2 >= 0, z = 1 + 0 + X2 + 0 mark(z) -{ 5 }-> a__f(0, X2, 0) :|: z = 1 + 2 + X2 + 2, X2 >= 0 mark(z) -{ 4 }-> a__f(0, X2, 0) :|: z = 1 + 2 + X2 + 0, X2 >= 0 mark(z) -{ 4 }-> a__f(0, X2, 0) :|: X2 >= 0, z = 1 + 0 + X2 + 2 mark(z) -{ 2 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 2 }-> 1 :|: z = 2 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 2 }-> 0 :|: z = 2 ---------------------------------------- (35) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: a__c -{ 1 }-> 2 :|: a__c -{ 1 }-> 1 :|: a__c -{ 1 }-> 0 :|: a__f(z, z', z'') -{ 3 }-> a__f(a__f(mark(X1'), X2', mark(X3')), 1 + X1' + X2' + X3', a__f(mark(X1'), X2', mark(X3'))) :|: X3' >= 0, X2' >= 0, X1' >= 0, z'' = 1 + X1' + X2' + X3', z' = 1, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(2, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(2, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(2, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(1, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(1, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(1, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 3 }-> a__f(1, 1, 1) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 5 }-> a__f(0, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(0, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 5 }-> a__f(0, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 3 }-> a__f(0, 0, 0) :|: z'' = 0, z' = 1, z = 0 a__f(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 mark(z) -{ 3 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, a__f(mark(X11), X21, mark(X31))) :|: X1'' >= 0, X11 >= 0, X21 >= 0, X3'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + (1 + X11 + X21 + X31), X31 >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 4 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 2) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 2, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 1) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 1, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 4 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 1) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 2, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 0) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 0, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 4 }-> a__f(a__f(mark(X1''), X2'', mark(X3'')), X2, 0) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2'' + X3'') + X2 + 2, X3'' >= 0, X2'' >= 0, X2 >= 0 mark(z) -{ 4 }-> a__f(2, X2, a__f(mark(X12), X22, mark(X32))) :|: z = 1 + 2 + X2 + (1 + X12 + X22 + X32), X12 >= 0, X22 >= 0, X32 >= 0, X2 >= 0 mark(z) -{ 5 }-> a__f(2, z - 5, 2) :|: z - 5 >= 0 mark(z) -{ 5 }-> a__f(2, z - 5, 1) :|: z - 5 >= 0 mark(z) -{ 5 }-> a__f(2, z - 5, 0) :|: z - 5 >= 0 mark(z) -{ 4 }-> a__f(2, z - 4, 1) :|: z - 4 >= 0 mark(z) -{ 4 }-> a__f(2, z - 3, 0) :|: z - 3 >= 0 mark(z) -{ 4 }-> a__f(1, X2, a__f(mark(X12), X22, mark(X32))) :|: z = 1 + 2 + X2 + (1 + X12 + X22 + X32), X12 >= 0, X22 >= 0, X32 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(1, X2, a__f(mark(X14), X24, mark(X34))) :|: z = 1 + 1 + X2 + (1 + X14 + X24 + X34), X2 >= 0, X14 >= 0, X24 >= 0, X34 >= 0 mark(z) -{ 5 }-> a__f(1, z - 5, 2) :|: z - 5 >= 0 mark(z) -{ 5 }-> a__f(1, z - 5, 1) :|: z - 5 >= 0 mark(z) -{ 5 }-> a__f(1, z - 5, 0) :|: z - 5 >= 0 mark(z) -{ 4 }-> a__f(1, z - 4, 2) :|: z - 4 >= 0 mark(z) -{ 4 }-> a__f(1, z - 4, 1) :|: z - 4 >= 0 mark(z) -{ 4 }-> a__f(1, z - 4, 0) :|: z - 4 >= 0 mark(z) -{ 3 }-> a__f(1, z - 3, 1) :|: z - 3 >= 0 mark(z) -{ 4 }-> a__f(1, z - 3, 0) :|: z - 3 >= 0 mark(z) -{ 3 }-> a__f(1, z - 2, 0) :|: z - 2 >= 0 mark(z) -{ 4 }-> a__f(0, X2, a__f(mark(X12), X22, mark(X32))) :|: z = 1 + 2 + X2 + (1 + X12 + X22 + X32), X12 >= 0, X22 >= 0, X32 >= 0, X2 >= 0 mark(z) -{ 3 }-> a__f(0, X2, a__f(mark(X13), X23, mark(X33))) :|: X33 >= 0, X2 >= 0, z = 1 + 0 + X2 + (1 + X13 + X23 + X33), X13 >= 0, X23 >= 0 mark(z) -{ 5 }-> a__f(0, z - 5, 2) :|: z - 5 >= 0 mark(z) -{ 5 }-> a__f(0, z - 5, 1) :|: z - 5 >= 0 mark(z) -{ 5 }-> a__f(0, z - 5, 0) :|: z - 5 >= 0 mark(z) -{ 4 }-> a__f(0, z - 4, 1) :|: z - 4 >= 0 mark(z) -{ 4 }-> a__f(0, z - 3, 2) :|: z - 3 >= 0 mark(z) -{ 4 }-> a__f(0, z - 3, 1) :|: z - 3 >= 0 mark(z) -{ 4 }-> a__f(0, z - 3, 0) :|: z - 3 >= 0 mark(z) -{ 3 }-> a__f(0, z - 2, 1) :|: z - 2 >= 0 mark(z) -{ 3 }-> a__f(0, z - 1, 0) :|: z - 1 >= 0 mark(z) -{ 2 }-> 2 :|: z = 2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 2 }-> 1 :|: z = 2 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 2 }-> 0 :|: z = 2 ---------------------------------------- (37) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(z0, z1, z2) -> c3 A__C -> c4 A__C -> c5 A__C -> c6 MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) MARK(c) -> c9(A__C) MARK(a) -> c10 MARK(b) -> c11 S tuples: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(z0, z1, z2) -> c3 A__C -> c4 A__C -> c5 A__C -> c6 MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) MARK(c) -> c9(A__C) MARK(a) -> c10 MARK(b) -> c11 K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, A__C, MARK_1 Compound Symbols: c1_2, c2_2, c3, c4, c5, c6, c7_2, c8_2, c9_1, c10, c11 ---------------------------------------- (39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing nodes: A__F(z0, z1, z2) -> c3 MARK(a) -> c10 A__C -> c6 MARK(b) -> c11 MARK(c) -> c9(A__C) A__C -> c5 A__C -> c4 ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) S tuples: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_2, c2_2, c7_2, c8_2 ---------------------------------------- (41) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (42) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) The (relative) TRS S consists of the following rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Rewrite Strategy: INNERMOST ---------------------------------------- (43) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (44) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (45) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (46) 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: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) [1] A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) [1] MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) [1] MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) [1] a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) [0] a__f(z0, z1, z2) -> f(z0, z1, z2) [0] a__c -> a [0] a__c -> b [0] a__c -> c [0] mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) [0] mark(c) -> a__c [0] mark(a) -> a [0] mark(b) -> b [0] Rewrite Strategy: INNERMOST ---------------------------------------- (47) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (48) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) [1] A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) [1] MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) [1] MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) [1] a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) [0] a__f(z0, z1, z2) -> f(z0, z1, z2) [0] a__c -> a [0] a__c -> b [0] a__c -> c [0] mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) [0] mark(c) -> a__c [0] mark(a) -> a [0] mark(b) -> b [0] The TRS has the following type information: A__F :: a:b:f:c -> a:b:f:c -> a:b:f:c -> c1:c2 a :: a:b:f:c b :: a:b:f:c c1 :: c1:c2 -> c7:c8 -> c1:c2 mark :: a:b:f:c -> a:b:f:c MARK :: a:b:f:c -> c7:c8 c2 :: c1:c2 -> c7:c8 -> c1:c2 f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c c7 :: c1:c2 -> c7:c8 -> c7:c8 c8 :: c1:c2 -> c7:c8 -> c7:c8 a__f :: a:b:f:c -> a:b:f:c -> a:b:f:c -> a:b:f:c a__c :: a:b:f:c c :: a:b:f:c Rewrite Strategy: INNERMOST ---------------------------------------- (49) 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: A__F_3 MARK_1 (c) The following functions are completely defined: a__f_3 a__c mark_1 Due to the following rules being added: a__f(v0, v1, v2) -> null_a__f [0] a__c -> null_a__c [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__f, null_a__c, null_mark, const, const1 ---------------------------------------- (50) 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: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) [1] A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) [1] MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) [1] MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) [1] a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) [0] a__f(z0, z1, z2) -> f(z0, z1, z2) [0] a__c -> a [0] a__c -> b [0] a__c -> c [0] mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) [0] mark(c) -> a__c [0] mark(a) -> a [0] mark(b) -> b [0] a__f(v0, v1, v2) -> null_a__f [0] a__c -> null_a__c [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__F :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> c1:c2 a :: a:b:f:c:null_a__f:null_a__c:null_mark b :: a:b:f:c:null_a__f:null_a__c:null_mark c1 :: c1:c2 -> c7:c8 -> c1:c2 mark :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark MARK :: a:b:f:c:null_a__f:null_a__c:null_mark -> c7:c8 c2 :: c1:c2 -> c7:c8 -> c1:c2 f :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark c7 :: c1:c2 -> c7:c8 -> c7:c8 c8 :: c1:c2 -> c7:c8 -> c7:c8 a__f :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark a__c :: a:b:f:c:null_a__f:null_a__c:null_mark c :: a:b:f:c:null_a__f:null_a__c:null_mark null_a__f :: a:b:f:c:null_a__f:null_a__c:null_mark null_a__c :: a:b:f:c:null_a__f:null_a__c:null_mark null_mark :: a:b:f:c:null_a__f:null_a__c:null_mark const :: c1:c2 const1 :: c7:c8 Rewrite Strategy: INNERMOST ---------------------------------------- (51) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (52) 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: A__F(a, b, f(z0', z1', z2')) -> c1(A__F(a__f(mark(z0'), z1', mark(z2')), f(z0', z1', z2'), a__f(mark(z0'), z1', mark(z2'))), MARK(f(z0', z1', z2'))) [1] A__F(a, b, f(z0', z1', z2')) -> c1(A__F(a__f(mark(z0'), z1', mark(z2')), f(z0', z1', z2'), null_mark), MARK(f(z0', z1', z2'))) [1] A__F(a, b, c) -> c1(A__F(a__c, c, a__c), MARK(c)) [1] A__F(a, b, c) -> c1(A__F(a__c, c, null_mark), MARK(c)) [1] A__F(a, b, a) -> c1(A__F(a, a, a), MARK(a)) [1] A__F(a, b, a) -> c1(A__F(a, a, null_mark), MARK(a)) [1] A__F(a, b, b) -> c1(A__F(b, b, b), MARK(b)) [1] A__F(a, b, b) -> c1(A__F(b, b, null_mark), MARK(b)) [1] A__F(a, b, f(z0'', z1'', z2'')) -> c1(A__F(null_mark, f(z0'', z1'', z2''), a__f(mark(z0''), z1'', mark(z2''))), MARK(f(z0'', z1'', z2''))) [1] A__F(a, b, c) -> c1(A__F(null_mark, c, a__c), MARK(c)) [1] A__F(a, b, a) -> c1(A__F(null_mark, a, a), MARK(a)) [1] A__F(a, b, b) -> c1(A__F(null_mark, b, b), MARK(b)) [1] A__F(a, b, z0) -> c1(A__F(null_mark, z0, null_mark), MARK(z0)) [1] A__F(a, b, f(z01, z11, z21)) -> c2(A__F(a__f(mark(z01), z11, mark(z21)), f(z01, z11, z21), a__f(mark(z01), z11, mark(z21))), MARK(f(z01, z11, z21))) [1] A__F(a, b, f(z01, z11, z21)) -> c2(A__F(a__f(mark(z01), z11, mark(z21)), f(z01, z11, z21), null_mark), MARK(f(z01, z11, z21))) [1] A__F(a, b, c) -> c2(A__F(a__c, c, a__c), MARK(c)) [1] A__F(a, b, c) -> c2(A__F(a__c, c, null_mark), MARK(c)) [1] A__F(a, b, a) -> c2(A__F(a, a, a), MARK(a)) [1] A__F(a, b, a) -> c2(A__F(a, a, null_mark), MARK(a)) [1] A__F(a, b, b) -> c2(A__F(b, b, b), MARK(b)) [1] A__F(a, b, b) -> c2(A__F(b, b, null_mark), MARK(b)) [1] A__F(a, b, f(z02, z12, z22)) -> c2(A__F(null_mark, f(z02, z12, z22), a__f(mark(z02), z12, mark(z22))), MARK(f(z02, z12, z22))) [1] A__F(a, b, c) -> c2(A__F(null_mark, c, a__c), MARK(c)) [1] A__F(a, b, a) -> c2(A__F(null_mark, a, a), MARK(a)) [1] A__F(a, b, b) -> c2(A__F(null_mark, b, b), MARK(b)) [1] A__F(a, b, z0) -> c2(A__F(null_mark, z0, null_mark), MARK(z0)) [1] MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) [1] MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) [1] a__f(a, b, f(z015, z115, z215)) -> a__f(a__f(mark(z015), z115, mark(z215)), f(z015, z115, z215), a__f(mark(z015), z115, mark(z215))) [0] a__f(a, b, f(z015, z115, z215)) -> a__f(a__f(mark(z015), z115, mark(z215)), f(z015, z115, z215), null_mark) [0] a__f(a, b, c) -> a__f(a__c, c, a__c) [0] a__f(a, b, c) -> a__f(a__c, c, null_mark) [0] a__f(a, b, a) -> a__f(a, a, a) [0] a__f(a, b, a) -> a__f(a, a, null_mark) [0] a__f(a, b, b) -> a__f(b, b, b) [0] a__f(a, b, b) -> a__f(b, b, null_mark) [0] a__f(a, b, f(z016, z116, z216)) -> a__f(null_mark, f(z016, z116, z216), a__f(mark(z016), z116, mark(z216))) [0] a__f(a, b, c) -> a__f(null_mark, c, a__c) [0] a__f(a, b, a) -> a__f(null_mark, a, a) [0] a__f(a, b, b) -> a__f(null_mark, b, b) [0] a__f(a, b, z0) -> a__f(null_mark, z0, null_mark) [0] a__f(z0, z1, z2) -> f(z0, z1, z2) [0] a__c -> a [0] a__c -> b [0] a__c -> c [0] mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) [0] mark(c) -> a__c [0] mark(a) -> a [0] mark(b) -> b [0] a__f(v0, v1, v2) -> null_a__f [0] a__c -> null_a__c [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__F :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> c1:c2 a :: a:b:f:c:null_a__f:null_a__c:null_mark b :: a:b:f:c:null_a__f:null_a__c:null_mark c1 :: c1:c2 -> c7:c8 -> c1:c2 mark :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark MARK :: a:b:f:c:null_a__f:null_a__c:null_mark -> c7:c8 c2 :: c1:c2 -> c7:c8 -> c1:c2 f :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark c7 :: c1:c2 -> c7:c8 -> c7:c8 c8 :: c1:c2 -> c7:c8 -> c7:c8 a__f :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark a__c :: a:b:f:c:null_a__f:null_a__c:null_mark c :: a:b:f:c:null_a__f:null_a__c:null_mark null_a__f :: a:b:f:c:null_a__f:null_a__c:null_mark null_a__c :: a:b:f:c:null_a__f:null_a__c:null_mark null_mark :: a:b:f:c:null_a__f:null_a__c:null_mark const :: c1:c2 const1 :: c7:c8 Rewrite Strategy: INNERMOST ---------------------------------------- (53) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: a => 0 b => 1 c => 2 null_a__f => 0 null_a__c => 0 null_mark => 0 const => 0 const1 => 0 ---------------------------------------- (54) Obligation: Complexity RNTS consisting of the following rules: A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z0'), z1', mark(z2')), 1 + z0' + z1' + z2', a__f(mark(z0'), z1', mark(z2'))) + MARK(1 + z0' + z1' + z2') :|: z0' >= 0, z'' = 1 + z0' + z1' + z2', z1' >= 0, z2' >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z0'), z1', mark(z2')), 1 + z0' + z1' + z2', 0) + MARK(1 + z0' + z1' + z2') :|: z0' >= 0, z'' = 1 + z0' + z1' + z2', z1' >= 0, z2' >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z01), z11, mark(z21)), 1 + z01 + z11 + z21, a__f(mark(z01), z11, mark(z21))) + MARK(1 + z01 + z11 + z21) :|: z21 >= 0, z11 >= 0, z'' = 1 + z01 + z11 + z21, z01 >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z01), z11, mark(z21)), 1 + z01 + z11 + z21, 0) + MARK(1 + z01 + z11 + z21) :|: z21 >= 0, z11 >= 0, z'' = 1 + z01 + z11 + z21, z01 >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__c, 2, a__c) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__c, 2, 0) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 1, 1) + MARK(1) :|: z' = 1, z = 0, z'' = 1 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 1, 0) + MARK(1) :|: z' = 1, z = 0, z'' = 1 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, z0, 0) + MARK(z0) :|: z'' = z0, z0 >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 2, a__c) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 1, 1) + MARK(1) :|: z' = 1, z = 0, z'' = 1 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 0, 0) + MARK(0) :|: z'' = 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 1 + z0'' + z1'' + z2'', a__f(mark(z0''), z1'', mark(z2''))) + MARK(1 + z0'' + z1'' + z2'') :|: z'' = 1 + z0'' + z1'' + z2'', z' = 1, z0'' >= 0, z = 0, z2'' >= 0, z1'' >= 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 1 + z02 + z12 + z22, a__f(mark(z02), z12, mark(z22))) + MARK(1 + z02 + z12 + z22) :|: z'' = 1 + z02 + z12 + z22, z02 >= 0, z12 >= 0, z' = 1, z22 >= 0, z = 0 MARK(z) -{ 1 }-> 1 + A__F(mark(z0), z1, mark(z2)) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__F(mark(z0), z1, mark(z2)) + MARK(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 a__c -{ 0 }-> 2 :|: a__c -{ 0 }-> 1 :|: a__c -{ 0 }-> 0 :|: a__f(z, z', z'') -{ 0 }-> a__f(a__f(mark(z015), z115, mark(z215)), 1 + z015 + z115 + z215, a__f(mark(z015), z115, mark(z215))) :|: z015 >= 0, z'' = 1 + z015 + z115 + z215, z115 >= 0, z' = 1, z = 0, z215 >= 0 a__f(z, z', z'') -{ 0 }-> a__f(a__f(mark(z015), z115, mark(z215)), 1 + z015 + z115 + z215, 0) :|: z015 >= 0, z'' = 1 + z015 + z115 + z215, z115 >= 0, z' = 1, z = 0, z215 >= 0 a__f(z, z', z'') -{ 0 }-> a__f(a__c, 2, a__c) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(a__c, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(1, 1, 1) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 0 }-> a__f(1, 1, 0) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 0 }-> a__f(0, z0, 0) :|: z'' = z0, z0 >= 0, z' = 1, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 2, a__c) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 1, 1) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 0 }-> a__f(0, 0, 0) :|: z'' = 0, z' = 1, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 1 + z016 + z116 + z216, a__f(mark(z016), z116, mark(z216))) :|: z216 >= 0, z'' = 1 + z016 + z116 + z216, z016 >= 0, z' = 1, z = 0, z116 >= 0 a__f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__f(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__f(mark(z0), z1, mark(z2)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__c :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 ---------------------------------------- (55) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__c -{ 0 }-> 0 :|: a__c -{ 0 }-> 1 :|: a__c -{ 0 }-> 2 :|: ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z0'), z1', mark(z2')), 1 + z0' + z1' + z2', a__f(mark(z0'), z1', mark(z2'))) + MARK(1 + z0' + z1' + z2') :|: z0' >= 0, z'' = 1 + z0' + z1' + z2', z1' >= 0, z2' >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z0'), z1', mark(z2')), 1 + z0' + z1' + z2', 0) + MARK(1 + z0' + z1' + z2') :|: z0' >= 0, z'' = 1 + z0' + z1' + z2', z1' >= 0, z2' >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z01), z11, mark(z21)), 1 + z01 + z11 + z21, a__f(mark(z01), z11, mark(z21))) + MARK(1 + z01 + z11 + z21) :|: z21 >= 0, z11 >= 0, z'' = 1 + z01 + z11 + z21, z01 >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z01), z11, mark(z21)), 1 + z01 + z11 + z21, 0) + MARK(1 + z01 + z11 + z21) :|: z21 >= 0, z11 >= 0, z'' = 1 + z01 + z11 + z21, z01 >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(2, 2, 2) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(2, 2, 1) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(2, 2, 0) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 2, 2) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 2, 1) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 2, 0) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 1, 1) + MARK(1) :|: z' = 1, z = 0, z'' = 1 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 1, 0) + MARK(1) :|: z' = 1, z = 0, z'' = 1 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, z0, 0) + MARK(z0) :|: z'' = z0, z0 >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 2, 2) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 2, 1) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 2, 0) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 1, 1) + MARK(1) :|: z' = 1, z = 0, z'' = 1 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 0, 0) + MARK(0) :|: z'' = 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 1 + z0'' + z1'' + z2'', a__f(mark(z0''), z1'', mark(z2''))) + MARK(1 + z0'' + z1'' + z2'') :|: z'' = 1 + z0'' + z1'' + z2'', z' = 1, z0'' >= 0, z = 0, z2'' >= 0, z1'' >= 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 1 + z02 + z12 + z22, a__f(mark(z02), z12, mark(z22))) + MARK(1 + z02 + z12 + z22) :|: z'' = 1 + z02 + z12 + z22, z02 >= 0, z12 >= 0, z' = 1, z22 >= 0, z = 0 MARK(z) -{ 1 }-> 1 + A__F(mark(z0), z1, mark(z2)) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__F(mark(z0), z1, mark(z2)) + MARK(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 a__c -{ 0 }-> 2 :|: a__c -{ 0 }-> 1 :|: a__c -{ 0 }-> 0 :|: a__f(z, z', z'') -{ 0 }-> a__f(a__f(mark(z015), z115, mark(z215)), 1 + z015 + z115 + z215, a__f(mark(z015), z115, mark(z215))) :|: z015 >= 0, z'' = 1 + z015 + z115 + z215, z115 >= 0, z' = 1, z = 0, z215 >= 0 a__f(z, z', z'') -{ 0 }-> a__f(a__f(mark(z015), z115, mark(z215)), 1 + z015 + z115 + z215, 0) :|: z015 >= 0, z'' = 1 + z015 + z115 + z215, z115 >= 0, z' = 1, z = 0, z215 >= 0 a__f(z, z', z'') -{ 0 }-> a__f(2, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(2, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(2, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(1, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(1, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(1, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(1, 1, 1) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 0 }-> a__f(1, 1, 0) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 0 }-> a__f(0, z0, 0) :|: z'' = z0, z0 >= 0, z' = 1, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 1, 1) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 0 }-> a__f(0, 0, 0) :|: z'' = 0, z' = 1, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 1 + z016 + z116 + z216, a__f(mark(z016), z116, mark(z216))) :|: z216 >= 0, z'' = 1 + z016 + z116 + z216, z016 >= 0, z' = 1, z = 0, z116 >= 0 a__f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__f(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__f(mark(z0), z1, mark(z2)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 1 :|: z = 2 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 0 :|: z = 2 ---------------------------------------- (57) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (58) Obligation: Complexity RNTS consisting of the following rules: A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z0'), z1', mark(z2')), 1 + z0' + z1' + z2', a__f(mark(z0'), z1', mark(z2'))) + MARK(1 + z0' + z1' + z2') :|: z0' >= 0, z'' = 1 + z0' + z1' + z2', z1' >= 0, z2' >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z0'), z1', mark(z2')), 1 + z0' + z1' + z2', 0) + MARK(1 + z0' + z1' + z2') :|: z0' >= 0, z'' = 1 + z0' + z1' + z2', z1' >= 0, z2' >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z01), z11, mark(z21)), 1 + z01 + z11 + z21, a__f(mark(z01), z11, mark(z21))) + MARK(1 + z01 + z11 + z21) :|: z21 >= 0, z11 >= 0, z'' = 1 + z01 + z11 + z21, z01 >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(a__f(mark(z01), z11, mark(z21)), 1 + z01 + z11 + z21, 0) + MARK(1 + z01 + z11 + z21) :|: z21 >= 0, z11 >= 0, z'' = 1 + z01 + z11 + z21, z01 >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(2, 2, 2) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(2, 2, 1) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(2, 2, 0) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 2, 2) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 2, 1) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 2, 0) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 1, 1) + MARK(1) :|: z' = 1, z = 0, z'' = 1 A__F(z, z', z'') -{ 1 }-> 1 + A__F(1, 1, 0) + MARK(1) :|: z' = 1, z = 0, z'' = 1 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, z'', 0) + MARK(z'') :|: z'' >= 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 2, 2) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 2, 1) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 2, 0) + MARK(2) :|: z' = 1, z'' = 2, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 1, 1) + MARK(1) :|: z' = 1, z = 0, z'' = 1 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 0, 0) + MARK(0) :|: z'' = 0, z' = 1, z = 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 1 + z0'' + z1'' + z2'', a__f(mark(z0''), z1'', mark(z2''))) + MARK(1 + z0'' + z1'' + z2'') :|: z'' = 1 + z0'' + z1'' + z2'', z' = 1, z0'' >= 0, z = 0, z2'' >= 0, z1'' >= 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(0, 1 + z02 + z12 + z22, a__f(mark(z02), z12, mark(z22))) + MARK(1 + z02 + z12 + z22) :|: z'' = 1 + z02 + z12 + z22, z02 >= 0, z12 >= 0, z' = 1, z22 >= 0, z = 0 MARK(z) -{ 1 }-> 1 + A__F(mark(z0), z1, mark(z2)) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__F(mark(z0), z1, mark(z2)) + MARK(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 a__c -{ 0 }-> 2 :|: a__c -{ 0 }-> 1 :|: a__c -{ 0 }-> 0 :|: a__f(z, z', z'') -{ 0 }-> a__f(a__f(mark(z015), z115, mark(z215)), 1 + z015 + z115 + z215, a__f(mark(z015), z115, mark(z215))) :|: z015 >= 0, z'' = 1 + z015 + z115 + z215, z115 >= 0, z' = 1, z = 0, z215 >= 0 a__f(z, z', z'') -{ 0 }-> a__f(a__f(mark(z015), z115, mark(z215)), 1 + z015 + z115 + z215, 0) :|: z015 >= 0, z'' = 1 + z015 + z115 + z215, z115 >= 0, z' = 1, z = 0, z215 >= 0 a__f(z, z', z'') -{ 0 }-> a__f(2, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(2, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(2, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(1, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(1, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(1, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(1, 1, 1) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 0 }-> a__f(1, 1, 0) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 0 }-> a__f(0, z'', 0) :|: z'' >= 0, z' = 1, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 2, 2) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 2, 1) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 2, 0) :|: z' = 1, z'' = 2, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 1, 1) :|: z' = 1, z = 0, z'' = 1 a__f(z, z', z'') -{ 0 }-> a__f(0, 0, 0) :|: z'' = 0, z' = 1, z = 0 a__f(z, z', z'') -{ 0 }-> a__f(0, 1 + z016 + z116 + z216, a__f(mark(z016), z116, mark(z216))) :|: z216 >= 0, z'' = 1 + z016 + z116 + z216, z016 >= 0, z' = 1, z = 0, z116 >= 0 a__f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__f(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0 mark(z) -{ 0 }-> a__f(mark(z0), z1, mark(z2)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> 2 :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 1 :|: z = 2 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 0 :|: z = 2 ---------------------------------------- (59) 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: a__f(v0, v1, v2) -> null_a__f [0] a__c -> null_a__c [0] mark(v0) -> null_mark [0] A__F(v0, v1, v2) -> null_A__F [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__f, null_a__c, null_mark, null_A__F, null_MARK ---------------------------------------- (60) 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: A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) [1] A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) [1] MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) [1] MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) [1] a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) [0] a__f(z0, z1, z2) -> f(z0, z1, z2) [0] a__c -> a [0] a__c -> b [0] a__c -> c [0] mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) [0] mark(c) -> a__c [0] mark(a) -> a [0] mark(b) -> b [0] a__f(v0, v1, v2) -> null_a__f [0] a__c -> null_a__c [0] mark(v0) -> null_mark [0] A__F(v0, v1, v2) -> null_A__F [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__F :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> c1:c2:null_A__F a :: a:b:f:c:null_a__f:null_a__c:null_mark b :: a:b:f:c:null_a__f:null_a__c:null_mark c1 :: c1:c2:null_A__F -> c7:c8:null_MARK -> c1:c2:null_A__F mark :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark MARK :: a:b:f:c:null_a__f:null_a__c:null_mark -> c7:c8:null_MARK c2 :: c1:c2:null_A__F -> c7:c8:null_MARK -> c1:c2:null_A__F f :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark c7 :: c1:c2:null_A__F -> c7:c8:null_MARK -> c7:c8:null_MARK c8 :: c1:c2:null_A__F -> c7:c8:null_MARK -> c7:c8:null_MARK a__f :: a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark -> a:b:f:c:null_a__f:null_a__c:null_mark a__c :: a:b:f:c:null_a__f:null_a__c:null_mark c :: a:b:f:c:null_a__f:null_a__c:null_mark null_a__f :: a:b:f:c:null_a__f:null_a__c:null_mark null_a__c :: a:b:f:c:null_a__f:null_a__c:null_mark null_mark :: a:b:f:c:null_a__f:null_a__c:null_mark null_A__F :: c1:c2:null_A__F null_MARK :: c7:c8:null_MARK Rewrite Strategy: INNERMOST ---------------------------------------- (61) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: a => 0 b => 1 c => 2 null_a__f => 0 null_a__c => 0 null_mark => 0 null_A__F => 0 null_MARK => 0 ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: A__F(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__F(z, z', z'') -{ 1 }-> 1 + A__F(mark(z0), z0, mark(z0)) + MARK(z0) :|: z'' = z0, z0 >= 0, z' = 1, z = 0 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + A__F(mark(z0), z1, mark(z2)) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__F(mark(z0), z1, mark(z2)) + MARK(z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 a__c -{ 0 }-> 2 :|: a__c -{ 0 }-> 1 :|: a__c -{ 0 }-> 0 :|: a__f(z, z', z'') -{ 0 }-> a__f(mark(z0), z0, mark(z0)) :|: z'' = z0, z0 >= 0, z' = 1, z = 0 a__f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__f(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__f(mark(z0), z1, mark(z2)) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__c :|: z = 2 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__F(a, b, z0) -> c1(A__F(mark(z0), z0, mark(z0)), MARK(z0)) by A__F(a, b, f(z0, z1, z2)) -> c1(A__F(mark(f(z0, z1, z2)), f(z0, z1, z2), a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c1(A__F(mark(c), c, a__c), MARK(c)) A__F(a, b, a) -> c1(A__F(mark(a), a, a), MARK(a)) A__F(a, b, b) -> c1(A__F(mark(b), b, b), MARK(b)) A__F(a, b, f(z0, z1, z2)) -> c1(A__F(a__f(mark(z0), z1, mark(z2)), f(z0, z1, z2), mark(f(z0, z1, z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c1(A__F(a__c, c, mark(c)), MARK(c)) A__F(a, b, a) -> c1(A__F(a, a, mark(a)), MARK(a)) A__F(a, b, b) -> c1(A__F(b, b, mark(b)), MARK(b)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(A__F(mark(f(z0, z1, z2)), f(z0, z1, z2), a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c1(A__F(mark(c), c, a__c), MARK(c)) A__F(a, b, a) -> c1(A__F(mark(a), a, a), MARK(a)) A__F(a, b, b) -> c1(A__F(mark(b), b, b), MARK(b)) A__F(a, b, f(z0, z1, z2)) -> c1(A__F(a__f(mark(z0), z1, mark(z2)), f(z0, z1, z2), mark(f(z0, z1, z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c1(A__F(a__c, c, mark(c)), MARK(c)) A__F(a, b, a) -> c1(A__F(a, a, mark(a)), MARK(a)) A__F(a, b, b) -> c1(A__F(b, b, mark(b)), MARK(b)) S tuples: A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(A__F(mark(f(z0, z1, z2)), f(z0, z1, z2), a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c1(A__F(mark(c), c, a__c), MARK(c)) A__F(a, b, a) -> c1(A__F(mark(a), a, a), MARK(a)) A__F(a, b, b) -> c1(A__F(mark(b), b, b), MARK(b)) A__F(a, b, f(z0, z1, z2)) -> c1(A__F(a__f(mark(z0), z1, mark(z2)), f(z0, z1, z2), mark(f(z0, z1, z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c1(A__F(a__c, c, mark(c)), MARK(c)) A__F(a, b, a) -> c1(A__F(a, a, mark(a)), MARK(a)) A__F(a, b, b) -> c1(A__F(b, b, mark(b)), MARK(b)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c2_2, c7_2, c8_2, c1_2 ---------------------------------------- (65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: A__F(a, b, b) -> c1(A__F(b, b, mark(b)), MARK(b)) A__F(a, b, c) -> c1(A__F(a__c, c, mark(c)), MARK(c)) A__F(a, b, a) -> c1(A__F(a, a, mark(a)), MARK(a)) A__F(a, b, c) -> c1(A__F(mark(c), c, a__c), MARK(c)) A__F(a, b, a) -> c1(A__F(mark(a), a, a), MARK(a)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(A__F(mark(f(z0, z1, z2)), f(z0, z1, z2), a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b), MARK(b)) A__F(a, b, f(z0, z1, z2)) -> c1(A__F(a__f(mark(z0), z1, mark(z2)), f(z0, z1, z2), mark(f(z0, z1, z2))), MARK(f(z0, z1, z2))) S tuples: A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(A__F(mark(f(z0, z1, z2)), f(z0, z1, z2), a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b), MARK(b)) A__F(a, b, f(z0, z1, z2)) -> c1(A__F(a__f(mark(z0), z1, mark(z2)), f(z0, z1, z2), mark(f(z0, z1, z2))), MARK(f(z0, z1, z2))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c2_2, c7_2, c8_2, c1_2 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) S tuples: A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c2_2, c7_2, c8_2, c1_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__F(a, b, z0) -> c2(A__F(mark(z0), z0, mark(z0)), MARK(z0)) by A__F(a, b, f(z0, z1, z2)) -> c2(A__F(mark(f(z0, z1, z2)), f(z0, z1, z2), a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c2(A__F(mark(c), c, a__c), MARK(c)) A__F(a, b, a) -> c2(A__F(mark(a), a, a), MARK(a)) A__F(a, b, b) -> c2(A__F(mark(b), b, b), MARK(b)) A__F(a, b, f(z0, z1, z2)) -> c2(A__F(a__f(mark(z0), z1, mark(z2)), f(z0, z1, z2), mark(f(z0, z1, z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c2(A__F(a__c, c, mark(c)), MARK(c)) A__F(a, b, a) -> c2(A__F(a, a, mark(a)), MARK(a)) A__F(a, b, b) -> c2(A__F(b, b, mark(b)), MARK(b)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(A__F(mark(f(z0, z1, z2)), f(z0, z1, z2), a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c2(A__F(mark(c), c, a__c), MARK(c)) A__F(a, b, a) -> c2(A__F(mark(a), a, a), MARK(a)) A__F(a, b, b) -> c2(A__F(mark(b), b, b), MARK(b)) A__F(a, b, f(z0, z1, z2)) -> c2(A__F(a__f(mark(z0), z1, mark(z2)), f(z0, z1, z2), mark(f(z0, z1, z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c2(A__F(a__c, c, mark(c)), MARK(c)) A__F(a, b, a) -> c2(A__F(a, a, mark(a)), MARK(a)) A__F(a, b, b) -> c2(A__F(b, b, mark(b)), MARK(b)) S tuples: MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(A__F(mark(f(z0, z1, z2)), f(z0, z1, z2), a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c2(A__F(mark(c), c, a__c), MARK(c)) A__F(a, b, a) -> c2(A__F(mark(a), a, a), MARK(a)) A__F(a, b, b) -> c2(A__F(mark(b), b, b), MARK(b)) A__F(a, b, f(z0, z1, z2)) -> c2(A__F(a__f(mark(z0), z1, mark(z2)), f(z0, z1, z2), mark(f(z0, z1, z2))), MARK(f(z0, z1, z2))) A__F(a, b, c) -> c2(A__F(a__c, c, mark(c)), MARK(c)) A__F(a, b, a) -> c2(A__F(a, a, mark(a)), MARK(a)) A__F(a, b, b) -> c2(A__F(b, b, mark(b)), MARK(b)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c7_2, c8_2, c1_1, c2_2 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: A__F(a, b, b) -> c2(A__F(b, b, mark(b)), MARK(b)) A__F(a, b, a) -> c2(A__F(mark(a), a, a), MARK(a)) A__F(a, b, c) -> c2(A__F(mark(c), c, a__c), MARK(c)) A__F(a, b, a) -> c2(A__F(a, a, mark(a)), MARK(a)) A__F(a, b, c) -> c2(A__F(a__c, c, mark(c)), MARK(c)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(A__F(mark(f(z0, z1, z2)), f(z0, z1, z2), a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b), MARK(b)) A__F(a, b, f(z0, z1, z2)) -> c2(A__F(a__f(mark(z0), z1, mark(z2)), f(z0, z1, z2), mark(f(z0, z1, z2))), MARK(f(z0, z1, z2))) S tuples: MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(A__F(mark(f(z0, z1, z2)), f(z0, z1, z2), a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b), MARK(b)) A__F(a, b, f(z0, z1, z2)) -> c2(A__F(a__f(mark(z0), z1, mark(z2)), f(z0, z1, z2), mark(f(z0, z1, z2))), MARK(f(z0, z1, z2))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c7_2, c8_2, c1_1, c2_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) S tuples: MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c7_2, c8_2, c1_1, c2_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(z0, z1, z2)) -> c7(A__F(mark(z0), z1, mark(z2)), MARK(z0)) by MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, a)) -> c7(A__F(mark(x0), x1, a), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2)), MARK(c)) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2)), MARK(a)) MARK(f(b, x1, x2)) -> c7(A__F(b, x1, mark(x2)), MARK(b)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, a)) -> c7(A__F(mark(x0), x1, a), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2)), MARK(c)) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2)), MARK(a)) MARK(f(b, x1, x2)) -> c7(A__F(b, x1, mark(x2)), MARK(b)) S tuples: MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, a)) -> c7(A__F(mark(x0), x1, a), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2)), MARK(c)) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2)), MARK(a)) MARK(f(b, x1, x2)) -> c7(A__F(b, x1, mark(x2)), MARK(b)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c8_2, c1_1, c2_1, c7_2 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(f(b, x1, x2)) -> c7(A__F(b, x1, mark(x2)), MARK(b)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, a)) -> c7(A__F(mark(x0), x1, a), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2)), MARK(c)) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2)), MARK(a)) S tuples: MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, a)) -> c7(A__F(mark(x0), x1, a), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2)), MARK(c)) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2)), MARK(a)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c8_2, c1_1, c2_1, c7_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) S tuples: MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c8_2, c1_1, c2_1, c7_2, c7_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(z0, z1, z2)) -> c8(A__F(mark(z0), z1, mark(z2)), MARK(z2)) by MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c), MARK(c)) MARK(f(x0, x1, a)) -> c8(A__F(mark(x0), x1, a), MARK(a)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b), MARK(b)) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(b, x1, x2)) -> c8(A__F(b, x1, mark(x2)), MARK(x2)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c), MARK(c)) MARK(f(x0, x1, a)) -> c8(A__F(mark(x0), x1, a), MARK(a)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b), MARK(b)) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(b, x1, x2)) -> c8(A__F(b, x1, mark(x2)), MARK(x2)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c), MARK(c)) MARK(f(x0, x1, a)) -> c8(A__F(mark(x0), x1, a), MARK(a)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b), MARK(b)) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(b, x1, x2)) -> c8(A__F(b, x1, mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(f(x0, x1, a)) -> c8(A__F(mark(x0), x1, a), MARK(a)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c), MARK(c)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b), MARK(b)) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(b, x1, x2)) -> c8(A__F(b, x1, mark(x2)), MARK(x2)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c), MARK(c)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b), MARK(b)) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(b, x1, x2)) -> c8(A__F(b, x1, mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c1(A__F(mark(b), b, b)) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__F(a, b, b) -> c1(A__F(mark(b), b, b)) by A__F(a, b, b) -> c1(A__F(b, b, b)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) A__F(a, b, b) -> c1(A__F(b, b, b)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) A__F(a, b, b) -> c1(A__F(b, b, b)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__F(a, b, b) -> c1(A__F(b, b, b)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) A__F(a, b, b) -> c2(A__F(mark(b), b, b)) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__F(a, b, b) -> c2(A__F(mark(b), b, b)) by A__F(a, b, b) -> c2(A__F(b, b, b)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) A__F(a, b, b) -> c2(A__F(b, b, b)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) A__F(a, b, b) -> c2(A__F(b, b, b)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__F(a, b, b) -> c2(A__F(b, b, b)) MARK(f(x0, x1, b)) -> c8(A__F(mark(x0), x1, b)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(x0, x1, b)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(x0, x1, f(z0, z1, z2))) -> c7(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(x0)) by MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(c)) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(a)) MARK(f(b, x1, f(x2, x3, x4))) -> c7(A__F(b, x1, a__f(mark(x2), x3, mark(x4))), MARK(b)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(c)) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(a)) MARK(f(b, x1, f(x2, x3, x4))) -> c7(A__F(b, x1, a__f(mark(x2), x3, mark(x4))), MARK(b)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(c)) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(a)) MARK(f(b, x1, f(x2, x3, x4))) -> c7(A__F(b, x1, a__f(mark(x2), x3, mark(x4))), MARK(b)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(f(b, x1, f(x2, x3, x4))) -> c7(A__F(b, x1, a__f(mark(x2), x3, mark(x4))), MARK(b)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(c)) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(a)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(c)) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(a)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a__c), MARK(x0)) by MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c), MARK(c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c), MARK(a)) MARK(f(b, x1, c)) -> c7(A__F(b, x1, a__c), MARK(b)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c), MARK(c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c), MARK(a)) MARK(f(b, x1, c)) -> c7(A__F(b, x1, a__c), MARK(b)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c), MARK(c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c), MARK(a)) MARK(f(b, x1, c)) -> c7(A__F(b, x1, a__c), MARK(b)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(f(b, x1, c)) -> c7(A__F(b, x1, a__c), MARK(b)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c), MARK(c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c), MARK(a)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, a), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, b), MARK(x0)) MARK(f(x0, x1, c)) -> c7(A__F(mark(x0), x1, c), MARK(x0)) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c), MARK(c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c), MARK(a)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(f(z0, z1, z2), x1, x2)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(f(z0, z1, z2))) by MARK(f(f(x0, x1, x2), x3, f(z0, z1, z2))) -> c7(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__f(mark(z0), z1, mark(z2))), MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, c)) -> c7(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c), MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(A__F(a__f(mark(x0), x1, mark(x2)), x3, a), MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(A__F(a__f(mark(x0), x1, mark(x2)), x3, b), MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(A__F(f(mark(x0), z1, mark(x2)), x3, mark(x4)), MARK(f(x0, z1, x2))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, x2), x3, a)) -> c7(A__F(a__f(mark(x0), x1, mark(x2)), x3, a), MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(A__F(a__f(mark(x0), x1, mark(x2)), x3, b), MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(A__F(f(mark(x0), z1, mark(x2)), x3, mark(x4)), MARK(f(x0, z1, x2))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, x2), x3, a)) -> c7(A__F(a__f(mark(x0), x1, mark(x2)), x3, a), MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(A__F(a__f(mark(x0), x1, mark(x2)), x3, b), MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(A__F(f(mark(x0), z1, mark(x2)), x3, mark(x4)), MARK(f(x0, z1, x2))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(c, x1, x2)) -> c7(A__F(a__c, x1, mark(x2))) by MARK(f(c, x0, f(z0, z1, z2))) -> c7(A__F(a__c, x0, a__f(mark(z0), z1, mark(z2)))) MARK(f(c, x0, c)) -> c7(A__F(a__c, x0, a__c)) MARK(f(c, x0, a)) -> c7(A__F(a__c, x0, a)) MARK(f(c, x0, b)) -> c7(A__F(a__c, x0, b)) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(c, x0, x1)) -> c7(A__F(b, x0, mark(x1))) MARK(f(c, x0, x1)) -> c7(A__F(c, x0, mark(x1))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, a)) -> c7(A__F(a__c, x0, a)) MARK(f(c, x0, b)) -> c7(A__F(a__c, x0, b)) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(c, x0, x1)) -> c7(A__F(b, x0, mark(x1))) MARK(f(c, x0, x1)) -> c7(A__F(c, x0, mark(x1))) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, a)) -> c7(A__F(a__c, x0, a)) MARK(f(c, x0, b)) -> c7(A__F(a__c, x0, b)) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(c, x0, x1)) -> c7(A__F(b, x0, mark(x1))) MARK(f(c, x0, x1)) -> c7(A__F(c, x0, mark(x1))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: MARK(f(c, x0, x1)) -> c7(A__F(b, x0, mark(x1))) MARK(f(c, x0, b)) -> c7(A__F(a__c, x0, b)) MARK(f(c, x0, a)) -> c7(A__F(a__c, x0, a)) MARK(f(c, x0, x1)) -> c7(A__F(c, x0, mark(x1))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(a, x1, x2)) -> c7(A__F(a, x1, mark(x2))) by MARK(f(a, x0, f(z0, z1, z2))) -> c7(A__F(a, x0, a__f(mark(z0), z1, mark(z2)))) MARK(f(a, x0, c)) -> c7(A__F(a, x0, a__c)) MARK(f(a, x0, a)) -> c7(A__F(a, x0, a)) MARK(f(a, x0, b)) -> c7(A__F(a, x0, b)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(a, x0, a)) -> c7(A__F(a, x0, a)) MARK(f(a, x0, b)) -> c7(A__F(a, x0, b)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(a, x0, a)) -> c7(A__F(a, x0, a)) MARK(f(a, x0, b)) -> c7(A__F(a, x0, b)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(f(a, x0, a)) -> c7(A__F(a, x0, a)) MARK(f(a, x0, b)) -> c7(A__F(a, x0, b)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(x0, x1, f(z0, z1, z2))) -> c8(A__F(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) by MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(A__F(b, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(A__F(b, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(A__F(b, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(f(z0, z1, z2), x1, x2)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), MARK(x2)) by MARK(f(f(x0, x1, x2), x3, f(z0, z1, z2))) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c), MARK(c)) MARK(f(f(x0, x1, x2), x3, a)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a), MARK(a)) MARK(f(f(x0, x1, x2), x3, b)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, b), MARK(b)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(A__F(f(mark(x0), z1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c), MARK(c)) MARK(f(f(x0, x1, x2), x3, a)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a), MARK(a)) MARK(f(f(x0, x1, x2), x3, b)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, b), MARK(b)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(A__F(f(mark(x0), z1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c), MARK(c)) MARK(f(f(x0, x1, x2), x3, a)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a), MARK(a)) MARK(f(f(x0, x1, x2), x3, b)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, b), MARK(b)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(A__F(f(mark(x0), z1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(f(f(x0, x1, x2), x3, b)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, b), MARK(b)) MARK(f(f(x0, x1, x2), x3, a)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a), MARK(a)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c), MARK(c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(A__F(f(mark(x0), z1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c), MARK(c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(A__F(f(mark(x0), z1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(c, x1, x2)) -> c8(A__F(a__c, x1, mark(x2)), MARK(x2)) by MARK(f(c, x0, f(z0, z1, z2))) -> c8(A__F(a__c, x0, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c), MARK(c)) MARK(f(c, x0, a)) -> c8(A__F(a__c, x0, a), MARK(a)) MARK(f(c, x0, b)) -> c8(A__F(a__c, x0, b), MARK(b)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, x1)) -> c8(A__F(b, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, x1)) -> c8(A__F(c, x0, mark(x1)), MARK(x1)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c), MARK(c)) MARK(f(c, x0, a)) -> c8(A__F(a__c, x0, a), MARK(a)) MARK(f(c, x0, b)) -> c8(A__F(a__c, x0, b), MARK(b)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, x1)) -> c8(A__F(b, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, x1)) -> c8(A__F(c, x0, mark(x1)), MARK(x1)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c), MARK(c)) MARK(f(c, x0, a)) -> c8(A__F(a__c, x0, a), MARK(a)) MARK(f(c, x0, b)) -> c8(A__F(a__c, x0, b), MARK(b)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, x1)) -> c8(A__F(b, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, x1)) -> c8(A__F(c, x0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(f(c, x0, a)) -> c8(A__F(a__c, x0, a), MARK(a)) MARK(f(c, x0, b)) -> c8(A__F(a__c, x0, b), MARK(b)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c), MARK(c)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, x1)) -> c8(A__F(b, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, x1)) -> c8(A__F(c, x0, mark(x1)), MARK(x1)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c), MARK(c)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, x1)) -> c8(A__F(b, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, x1)) -> c8(A__F(c, x0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_2, c8_1, c7_2 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(a, x1, x2)) -> c8(A__F(a, x1, mark(x2)), MARK(x2)) by MARK(f(a, x0, f(z0, z1, z2))) -> c8(A__F(a, x0, a__f(mark(z0), z1, mark(z2))), MARK(f(z0, z1, z2))) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c), MARK(c)) MARK(f(a, x0, a)) -> c8(A__F(a, x0, a), MARK(a)) MARK(f(a, x0, b)) -> c8(A__F(a, x0, b), MARK(b)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c), MARK(c)) MARK(f(a, x0, a)) -> c8(A__F(a, x0, a), MARK(a)) MARK(f(a, x0, b)) -> c8(A__F(a, x0, b), MARK(b)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c), MARK(c)) MARK(f(a, x0, a)) -> c8(A__F(a, x0, a), MARK(a)) MARK(f(a, x0, b)) -> c8(A__F(a, x0, b), MARK(b)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(f(a, x0, b)) -> c8(A__F(a, x0, b), MARK(b)) MARK(f(a, x0, a)) -> c8(A__F(a, x0, a), MARK(a)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c), MARK(c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c), MARK(c)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a__c)) by MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, b)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, c)) MARK(f(f(z0, z1, z2), x1, c)) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c)) MARK(f(c, x1, c)) -> c8(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c8(A__F(a, x1, a__c)) MARK(f(b, x1, c)) -> c8(A__F(b, x1, a__c)) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, b)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, c)) MARK(f(b, x1, c)) -> c8(A__F(b, x1, a__c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, b)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, c)) MARK(f(b, x1, c)) -> c8(A__F(b, x1, a__c)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: MARK(f(b, x1, c)) -> c8(A__F(b, x1, a__c)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, a)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, b)) MARK(f(x0, x1, c)) -> c8(A__F(mark(x0), x1, c)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) by MARK(f(a, x0, c)) -> c7(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, c)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(a, x1, c)) -> c7(A__F(a, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, c)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(f(a, x0, c)) -> c7(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, c)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(a, x0, c)) -> c7(A__F(a, x0, a__c)) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(a, x0, c)) -> c7(A__F(a, x0, a__c)) by MARK(f(a, x0, c)) -> c7(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, c)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (153) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(f(a, x0, c)) -> c7(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c7(A__F(a, x0, c)) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) by MARK(f(a, x0, c)) -> c8(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, c)) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a__c)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, c)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(f(a, x0, c)) -> c8(A__F(a, x0, c)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, b)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x1, c)) -> c8(A__F(a, x1, a__c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(f(a, x1, c)) -> c8(A__F(a, x1, a__c)) by MARK(f(a, x0, c)) -> c8(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, c)) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, c)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: MARK(f(a, x0, c)) -> c8(A__F(a, x0, b)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, a)) MARK(f(a, x0, c)) -> c8(A__F(a, x0, c)) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) S tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (163) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) by A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) S tuples: A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c1_1, c2_1, c7_1, c8_1, c7_2, c8_2 ---------------------------------------- (165) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__F(a, b, f(z0, z1, z2)) -> c1(MARK(f(z0, z1, z2))) by A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) S tuples: A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c2_1, c7_1, c8_1, c7_2, c8_2, c1_1 ---------------------------------------- (167) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) by A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) S tuples: MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: A__F_3, MARK_1 Compound Symbols: c2_1, c7_1, c8_1, c7_2, c8_2, c1_1 ---------------------------------------- (169) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__F(a, b, f(z0, z1, z2)) -> c2(MARK(f(z0, z1, z2))) by A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) S tuples: MARK(f(x0, x1, a)) -> c7(MARK(x0)) MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c7_1, c8_1, c7_2, c8_2, c1_1, c2_1 ---------------------------------------- (171) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(f(x0, x1, a)) -> c7(MARK(x0)) by MARK(f(f(y0, y1, a), z1, a)) -> c7(MARK(f(y0, y1, a))) MARK(f(f(b, y0, y1), z1, a)) -> c7(MARK(f(b, y0, y1))) MARK(f(f(y0, y1, b), z1, a)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, a)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, a)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, a)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, a)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, a)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, a)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) MARK(f(f(y0, y1, a), z1, a)) -> c7(MARK(f(y0, y1, a))) MARK(f(f(b, y0, y1), z1, a)) -> c7(MARK(f(b, y0, y1))) MARK(f(f(y0, y1, b), z1, a)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, a)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, a)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, a)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, a)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, a)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, a)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) S tuples: MARK(f(b, x1, x2)) -> c8(MARK(x2)) MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) MARK(f(f(y0, y1, a), z1, a)) -> c7(MARK(f(y0, y1, a))) MARK(f(f(b, y0, y1), z1, a)) -> c7(MARK(f(b, y0, y1))) MARK(f(f(y0, y1, b), z1, a)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, a)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, a)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, a)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, a)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, a)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, a)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c8_1, c7_1, c7_2, c8_2, c1_1, c2_1 ---------------------------------------- (173) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(f(b, x1, x2)) -> c8(MARK(x2)) by MARK(f(b, z0, f(b, y0, y1))) -> c8(MARK(f(b, y0, y1))) MARK(f(b, z0, f(y0, y1, b))) -> c8(MARK(f(y0, y1, b))) MARK(f(b, z0, f(y0, y1, f(y2, y3, y4)))) -> c8(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, f(y4, y5, y6))))) -> c8(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(b, z0, f(y0, y1, f(y2, y3, c)))) -> c8(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, a)))) -> c8(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, b)))) -> c8(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(b, z0, f(y0, y1, f(f(y2, y3, y4), y5, y6)))) -> c8(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(b, z0, f(y0, y1, f(c, y2, y3)))) -> c8(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(a, y2, y3)))) -> c8(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(b, y2, y3)))) -> c8(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, f(y4, y5, y6)))) -> c8(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(b, z0, f(c, y0, f(y1, y2, y3)))) -> c8(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(a, y0, f(y1, y2, y3)))) -> c8(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, c))) -> c8(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(b, z0, f(y0, y1, c))) -> c8(MARK(f(y0, y1, c))) MARK(f(b, z0, f(c, y0, c))) -> c8(MARK(f(c, y0, c))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, y6))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(b, z0, f(f(y0, y1, c), y2, y3))) -> c8(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(b, z0, f(f(y0, y1, a), y2, y3))) -> c8(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(b, z0, f(f(y0, y1, b), y2, y3))) -> c8(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, y6))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(b, z0, f(f(c, y0, y1), y2, y3))) -> c8(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(b, z0, f(f(a, y0, y1), y2, y3))) -> c8(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(b, z0, f(f(b, y0, y1), y2, y3))) -> c8(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(b, z0, f(f(y0, y1, y2), y3, a))) -> c8(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(b, z0, f(f(y0, y1, y2), y3, b))) -> c8(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(b, z0, f(f(y0, y1, y2), y3, y4))) -> c8(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(b, z0, f(c, y0, y1))) -> c8(MARK(f(c, y0, y1))) MARK(f(b, z0, f(b, y0, f(y1, y2, y3)))) -> c8(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, a), y2, a))) -> c8(MARK(f(f(y0, y1, a), y2, a))) MARK(f(b, z0, f(f(b, y0, y1), y2, a))) -> c8(MARK(f(f(b, y0, y1), y2, a))) MARK(f(b, z0, f(f(y0, y1, b), y2, a))) -> c8(MARK(f(f(y0, y1, b), y2, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, c)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, a)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, b)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) -> c8(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(c, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(a, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(b, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(b, z0, f(f(c, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(a, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, c), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(b, z0, f(f(y0, y1, c), y2, a))) -> c8(MARK(f(f(y0, y1, c), y2, a))) MARK(f(b, z0, f(f(c, y0, c), y1, a))) -> c8(MARK(f(f(c, y0, c), y1, a))) MARK(f(b, z0, f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) -> c8(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(y0, y1, c), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, a), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, b), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) -> c8(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(c, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(a, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(b, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, a), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, b), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(b, z0, f(f(c, y0, y1), y2, a))) -> c8(MARK(f(f(c, y0, y1), y2, a))) MARK(f(b, z0, f(f(b, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) MARK(f(f(y0, y1, a), z1, a)) -> c7(MARK(f(y0, y1, a))) MARK(f(f(b, y0, y1), z1, a)) -> c7(MARK(f(b, y0, y1))) MARK(f(f(y0, y1, b), z1, a)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, a)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, a)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, a)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, a)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, a)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, a)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(b, y0, y1))) -> c8(MARK(f(b, y0, y1))) MARK(f(b, z0, f(y0, y1, b))) -> c8(MARK(f(y0, y1, b))) MARK(f(b, z0, f(y0, y1, f(y2, y3, y4)))) -> c8(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, f(y4, y5, y6))))) -> c8(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(b, z0, f(y0, y1, f(y2, y3, c)))) -> c8(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, a)))) -> c8(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, b)))) -> c8(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(b, z0, f(y0, y1, f(f(y2, y3, y4), y5, y6)))) -> c8(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(b, z0, f(y0, y1, f(c, y2, y3)))) -> c8(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(a, y2, y3)))) -> c8(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(b, y2, y3)))) -> c8(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, f(y4, y5, y6)))) -> c8(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(b, z0, f(c, y0, f(y1, y2, y3)))) -> c8(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(a, y0, f(y1, y2, y3)))) -> c8(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, c))) -> c8(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(b, z0, f(y0, y1, c))) -> c8(MARK(f(y0, y1, c))) MARK(f(b, z0, f(c, y0, c))) -> c8(MARK(f(c, y0, c))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, y6))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(b, z0, f(f(y0, y1, c), y2, y3))) -> c8(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(b, z0, f(f(y0, y1, a), y2, y3))) -> c8(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(b, z0, f(f(y0, y1, b), y2, y3))) -> c8(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, y6))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(b, z0, f(f(c, y0, y1), y2, y3))) -> c8(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(b, z0, f(f(a, y0, y1), y2, y3))) -> c8(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(b, z0, f(f(b, y0, y1), y2, y3))) -> c8(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(b, z0, f(f(y0, y1, y2), y3, a))) -> c8(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(b, z0, f(f(y0, y1, y2), y3, b))) -> c8(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(b, z0, f(f(y0, y1, y2), y3, y4))) -> c8(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(b, z0, f(c, y0, y1))) -> c8(MARK(f(c, y0, y1))) MARK(f(b, z0, f(b, y0, f(y1, y2, y3)))) -> c8(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, a), y2, a))) -> c8(MARK(f(f(y0, y1, a), y2, a))) MARK(f(b, z0, f(f(b, y0, y1), y2, a))) -> c8(MARK(f(f(b, y0, y1), y2, a))) MARK(f(b, z0, f(f(y0, y1, b), y2, a))) -> c8(MARK(f(f(y0, y1, b), y2, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, c)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, a)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, b)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) -> c8(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(c, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(a, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(b, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(b, z0, f(f(c, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(a, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, c), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(b, z0, f(f(y0, y1, c), y2, a))) -> c8(MARK(f(f(y0, y1, c), y2, a))) MARK(f(b, z0, f(f(c, y0, c), y1, a))) -> c8(MARK(f(f(c, y0, c), y1, a))) MARK(f(b, z0, f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) -> c8(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(y0, y1, c), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, a), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, b), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) -> c8(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(c, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(a, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(b, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, a), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, b), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(b, z0, f(f(c, y0, y1), y2, a))) -> c8(MARK(f(f(c, y0, y1), y2, a))) MARK(f(b, z0, f(f(b, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) S tuples: MARK(f(x0, x1, b)) -> c7(MARK(x0)) MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) MARK(f(f(y0, y1, a), z1, a)) -> c7(MARK(f(y0, y1, a))) MARK(f(f(b, y0, y1), z1, a)) -> c7(MARK(f(b, y0, y1))) MARK(f(f(y0, y1, b), z1, a)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, a)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, a)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, a)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, a)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, a)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, a)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(b, y0, y1))) -> c8(MARK(f(b, y0, y1))) MARK(f(b, z0, f(y0, y1, b))) -> c8(MARK(f(y0, y1, b))) MARK(f(b, z0, f(y0, y1, f(y2, y3, y4)))) -> c8(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, f(y4, y5, y6))))) -> c8(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(b, z0, f(y0, y1, f(y2, y3, c)))) -> c8(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, a)))) -> c8(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, b)))) -> c8(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(b, z0, f(y0, y1, f(f(y2, y3, y4), y5, y6)))) -> c8(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(b, z0, f(y0, y1, f(c, y2, y3)))) -> c8(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(a, y2, y3)))) -> c8(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(b, y2, y3)))) -> c8(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, f(y4, y5, y6)))) -> c8(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(b, z0, f(c, y0, f(y1, y2, y3)))) -> c8(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(a, y0, f(y1, y2, y3)))) -> c8(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, c))) -> c8(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(b, z0, f(y0, y1, c))) -> c8(MARK(f(y0, y1, c))) MARK(f(b, z0, f(c, y0, c))) -> c8(MARK(f(c, y0, c))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, y6))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(b, z0, f(f(y0, y1, c), y2, y3))) -> c8(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(b, z0, f(f(y0, y1, a), y2, y3))) -> c8(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(b, z0, f(f(y0, y1, b), y2, y3))) -> c8(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, y6))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(b, z0, f(f(c, y0, y1), y2, y3))) -> c8(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(b, z0, f(f(a, y0, y1), y2, y3))) -> c8(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(b, z0, f(f(b, y0, y1), y2, y3))) -> c8(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(b, z0, f(f(y0, y1, y2), y3, a))) -> c8(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(b, z0, f(f(y0, y1, y2), y3, b))) -> c8(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(b, z0, f(f(y0, y1, y2), y3, y4))) -> c8(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(b, z0, f(c, y0, y1))) -> c8(MARK(f(c, y0, y1))) MARK(f(b, z0, f(b, y0, f(y1, y2, y3)))) -> c8(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, a), y2, a))) -> c8(MARK(f(f(y0, y1, a), y2, a))) MARK(f(b, z0, f(f(b, y0, y1), y2, a))) -> c8(MARK(f(f(b, y0, y1), y2, a))) MARK(f(b, z0, f(f(y0, y1, b), y2, a))) -> c8(MARK(f(f(y0, y1, b), y2, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, c)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, a)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, b)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) -> c8(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(c, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(a, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(b, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(b, z0, f(f(c, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(a, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, c), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(b, z0, f(f(y0, y1, c), y2, a))) -> c8(MARK(f(f(y0, y1, c), y2, a))) MARK(f(b, z0, f(f(c, y0, c), y1, a))) -> c8(MARK(f(f(c, y0, c), y1, a))) MARK(f(b, z0, f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) -> c8(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(y0, y1, c), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, a), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, b), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) -> c8(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(c, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(a, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(b, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, a), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, b), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(b, z0, f(f(c, y0, y1), y2, a))) -> c8(MARK(f(f(c, y0, y1), y2, a))) MARK(f(b, z0, f(f(b, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c7_1, c7_2, c8_2, c8_1, c1_1, c2_1 ---------------------------------------- (175) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(f(x0, x1, b)) -> c7(MARK(x0)) by MARK(f(f(y0, y1, b), z1, b)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, b)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, b)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, b)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, b)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, b)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) MARK(f(f(y0, y1, a), z1, a)) -> c7(MARK(f(y0, y1, a))) MARK(f(f(b, y0, y1), z1, a)) -> c7(MARK(f(b, y0, y1))) MARK(f(f(y0, y1, b), z1, a)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, a)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, a)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, a)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, a)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, a)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, a)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(b, y0, y1))) -> c8(MARK(f(b, y0, y1))) MARK(f(b, z0, f(y0, y1, b))) -> c8(MARK(f(y0, y1, b))) MARK(f(b, z0, f(y0, y1, f(y2, y3, y4)))) -> c8(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, f(y4, y5, y6))))) -> c8(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(b, z0, f(y0, y1, f(y2, y3, c)))) -> c8(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, a)))) -> c8(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, b)))) -> c8(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(b, z0, f(y0, y1, f(f(y2, y3, y4), y5, y6)))) -> c8(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(b, z0, f(y0, y1, f(c, y2, y3)))) -> c8(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(a, y2, y3)))) -> c8(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(b, y2, y3)))) -> c8(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, f(y4, y5, y6)))) -> c8(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(b, z0, f(c, y0, f(y1, y2, y3)))) -> c8(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(a, y0, f(y1, y2, y3)))) -> c8(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, c))) -> c8(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(b, z0, f(y0, y1, c))) -> c8(MARK(f(y0, y1, c))) MARK(f(b, z0, f(c, y0, c))) -> c8(MARK(f(c, y0, c))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, y6))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(b, z0, f(f(y0, y1, c), y2, y3))) -> c8(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(b, z0, f(f(y0, y1, a), y2, y3))) -> c8(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(b, z0, f(f(y0, y1, b), y2, y3))) -> c8(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, y6))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(b, z0, f(f(c, y0, y1), y2, y3))) -> c8(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(b, z0, f(f(a, y0, y1), y2, y3))) -> c8(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(b, z0, f(f(b, y0, y1), y2, y3))) -> c8(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(b, z0, f(f(y0, y1, y2), y3, a))) -> c8(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(b, z0, f(f(y0, y1, y2), y3, b))) -> c8(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(b, z0, f(f(y0, y1, y2), y3, y4))) -> c8(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(b, z0, f(c, y0, y1))) -> c8(MARK(f(c, y0, y1))) MARK(f(b, z0, f(b, y0, f(y1, y2, y3)))) -> c8(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, a), y2, a))) -> c8(MARK(f(f(y0, y1, a), y2, a))) MARK(f(b, z0, f(f(b, y0, y1), y2, a))) -> c8(MARK(f(f(b, y0, y1), y2, a))) MARK(f(b, z0, f(f(y0, y1, b), y2, a))) -> c8(MARK(f(f(y0, y1, b), y2, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, c)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, a)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, b)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) -> c8(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(c, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(a, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(b, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(b, z0, f(f(c, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(a, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, c), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(b, z0, f(f(y0, y1, c), y2, a))) -> c8(MARK(f(f(y0, y1, c), y2, a))) MARK(f(b, z0, f(f(c, y0, c), y1, a))) -> c8(MARK(f(f(c, y0, c), y1, a))) MARK(f(b, z0, f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) -> c8(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(y0, y1, c), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, a), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, b), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) -> c8(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(c, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(a, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(b, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, a), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, b), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(b, z0, f(f(c, y0, y1), y2, a))) -> c8(MARK(f(f(c, y0, y1), y2, a))) MARK(f(b, z0, f(f(b, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(y0, y1, b), z1, b)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, b)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, b)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, b)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, b)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, b)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) S tuples: MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) MARK(f(f(y0, y1, a), z1, a)) -> c7(MARK(f(y0, y1, a))) MARK(f(f(b, y0, y1), z1, a)) -> c7(MARK(f(b, y0, y1))) MARK(f(f(y0, y1, b), z1, a)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, a)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, a)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, a)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, a)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, a)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, a)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(b, y0, y1))) -> c8(MARK(f(b, y0, y1))) MARK(f(b, z0, f(y0, y1, b))) -> c8(MARK(f(y0, y1, b))) MARK(f(b, z0, f(y0, y1, f(y2, y3, y4)))) -> c8(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, f(y4, y5, y6))))) -> c8(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(b, z0, f(y0, y1, f(y2, y3, c)))) -> c8(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, a)))) -> c8(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, b)))) -> c8(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(b, z0, f(y0, y1, f(f(y2, y3, y4), y5, y6)))) -> c8(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(b, z0, f(y0, y1, f(c, y2, y3)))) -> c8(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(a, y2, y3)))) -> c8(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(b, y2, y3)))) -> c8(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, f(y4, y5, y6)))) -> c8(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(b, z0, f(c, y0, f(y1, y2, y3)))) -> c8(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(a, y0, f(y1, y2, y3)))) -> c8(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, c))) -> c8(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(b, z0, f(y0, y1, c))) -> c8(MARK(f(y0, y1, c))) MARK(f(b, z0, f(c, y0, c))) -> c8(MARK(f(c, y0, c))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, y6))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(b, z0, f(f(y0, y1, c), y2, y3))) -> c8(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(b, z0, f(f(y0, y1, a), y2, y3))) -> c8(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(b, z0, f(f(y0, y1, b), y2, y3))) -> c8(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, y6))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(b, z0, f(f(c, y0, y1), y2, y3))) -> c8(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(b, z0, f(f(a, y0, y1), y2, y3))) -> c8(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(b, z0, f(f(b, y0, y1), y2, y3))) -> c8(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(b, z0, f(f(y0, y1, y2), y3, a))) -> c8(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(b, z0, f(f(y0, y1, y2), y3, b))) -> c8(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(b, z0, f(f(y0, y1, y2), y3, y4))) -> c8(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(b, z0, f(c, y0, y1))) -> c8(MARK(f(c, y0, y1))) MARK(f(b, z0, f(b, y0, f(y1, y2, y3)))) -> c8(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, a), y2, a))) -> c8(MARK(f(f(y0, y1, a), y2, a))) MARK(f(b, z0, f(f(b, y0, y1), y2, a))) -> c8(MARK(f(f(b, y0, y1), y2, a))) MARK(f(b, z0, f(f(y0, y1, b), y2, a))) -> c8(MARK(f(f(y0, y1, b), y2, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, c)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, a)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, b)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) -> c8(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(c, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(a, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(b, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(b, z0, f(f(c, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(a, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, c), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(b, z0, f(f(y0, y1, c), y2, a))) -> c8(MARK(f(f(y0, y1, c), y2, a))) MARK(f(b, z0, f(f(c, y0, c), y1, a))) -> c8(MARK(f(f(c, y0, c), y1, a))) MARK(f(b, z0, f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) -> c8(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(y0, y1, c), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, a), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, b), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) -> c8(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(c, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(a, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(b, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, a), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, b), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(b, z0, f(f(c, y0, y1), y2, a))) -> c8(MARK(f(f(c, y0, y1), y2, a))) MARK(f(b, z0, f(f(b, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(y0, y1, b), z1, b)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, b)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, b)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, b)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, b)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, b)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c7_2, c7_1, c8_2, c8_1, c1_1, c2_1 ---------------------------------------- (177) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(f(x0, x1, c)) -> c7(MARK(x0)) by MARK(f(f(y0, y1, f(y2, y3, y4)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, c)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, c)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, c)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, c)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(f(y0, y1, b), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, b))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, b))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, b))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, b))) MARK(f(f(f(y0, y1, c), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, b))) MARK(f(f(f(c, y0, c), y1, b), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, b))) MARK(f(f(f(c, y0, y1), y2, b), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, b))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, a), y3, b))) MARK(f(f(f(f(b, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, b), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, c), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, a), y3, b))) MARK(f(f(f(f(c, y0, c), y1, a), y2, b), z1, c)) -> c7(MARK(f(f(f(c, y0, c), y1, a), y2, b))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b))) MARK(f(f(f(f(c, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(b, y0, f(b, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, b)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, b)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, c)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, c)), y3, b))) MARK(f(f(f(b, y0, f(c, y1, c)), y2, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, c)), y2, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b))) MARK(f(f(f(b, y0, f(c, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) MARK(f(f(y0, y1, a), z1, a)) -> c7(MARK(f(y0, y1, a))) MARK(f(f(b, y0, y1), z1, a)) -> c7(MARK(f(b, y0, y1))) MARK(f(f(y0, y1, b), z1, a)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, a)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, a)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, a)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, a)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, a)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, a)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(b, y0, y1))) -> c8(MARK(f(b, y0, y1))) MARK(f(b, z0, f(y0, y1, b))) -> c8(MARK(f(y0, y1, b))) MARK(f(b, z0, f(y0, y1, f(y2, y3, y4)))) -> c8(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, f(y4, y5, y6))))) -> c8(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(b, z0, f(y0, y1, f(y2, y3, c)))) -> c8(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, a)))) -> c8(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, b)))) -> c8(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(b, z0, f(y0, y1, f(f(y2, y3, y4), y5, y6)))) -> c8(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(b, z0, f(y0, y1, f(c, y2, y3)))) -> c8(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(a, y2, y3)))) -> c8(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(b, y2, y3)))) -> c8(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, f(y4, y5, y6)))) -> c8(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(b, z0, f(c, y0, f(y1, y2, y3)))) -> c8(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(a, y0, f(y1, y2, y3)))) -> c8(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, c))) -> c8(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(b, z0, f(y0, y1, c))) -> c8(MARK(f(y0, y1, c))) MARK(f(b, z0, f(c, y0, c))) -> c8(MARK(f(c, y0, c))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, y6))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(b, z0, f(f(y0, y1, c), y2, y3))) -> c8(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(b, z0, f(f(y0, y1, a), y2, y3))) -> c8(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(b, z0, f(f(y0, y1, b), y2, y3))) -> c8(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, y6))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(b, z0, f(f(c, y0, y1), y2, y3))) -> c8(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(b, z0, f(f(a, y0, y1), y2, y3))) -> c8(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(b, z0, f(f(b, y0, y1), y2, y3))) -> c8(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(b, z0, f(f(y0, y1, y2), y3, a))) -> c8(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(b, z0, f(f(y0, y1, y2), y3, b))) -> c8(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(b, z0, f(f(y0, y1, y2), y3, y4))) -> c8(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(b, z0, f(c, y0, y1))) -> c8(MARK(f(c, y0, y1))) MARK(f(b, z0, f(b, y0, f(y1, y2, y3)))) -> c8(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, a), y2, a))) -> c8(MARK(f(f(y0, y1, a), y2, a))) MARK(f(b, z0, f(f(b, y0, y1), y2, a))) -> c8(MARK(f(f(b, y0, y1), y2, a))) MARK(f(b, z0, f(f(y0, y1, b), y2, a))) -> c8(MARK(f(f(y0, y1, b), y2, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, c)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, a)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, b)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) -> c8(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(c, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(a, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(b, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(b, z0, f(f(c, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(a, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, c), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(b, z0, f(f(y0, y1, c), y2, a))) -> c8(MARK(f(f(y0, y1, c), y2, a))) MARK(f(b, z0, f(f(c, y0, c), y1, a))) -> c8(MARK(f(f(c, y0, c), y1, a))) MARK(f(b, z0, f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) -> c8(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(y0, y1, c), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, a), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, b), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) -> c8(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(c, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(a, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(b, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, a), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, b), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(b, z0, f(f(c, y0, y1), y2, a))) -> c8(MARK(f(f(c, y0, y1), y2, a))) MARK(f(b, z0, f(f(b, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(y0, y1, b), z1, b)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, b)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, b)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, b)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, b)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, b)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, c)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, c)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, c)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, c)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(f(y0, y1, b), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, b))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, b))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, b))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, b))) MARK(f(f(f(y0, y1, c), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, b))) MARK(f(f(f(c, y0, c), y1, b), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, b))) MARK(f(f(f(c, y0, y1), y2, b), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, b))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, a), y3, b))) MARK(f(f(f(f(b, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, b), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, c), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, a), y3, b))) MARK(f(f(f(f(c, y0, c), y1, a), y2, b), z1, c)) -> c7(MARK(f(f(f(c, y0, c), y1, a), y2, b))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b))) MARK(f(f(f(f(c, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(b, y0, f(b, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, b)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, b)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, c)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, c)), y3, b))) MARK(f(f(f(b, y0, f(c, y1, c)), y2, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, c)), y2, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b))) MARK(f(f(f(b, y0, f(c, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b))) S tuples: MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) MARK(f(f(y0, y1, a), z1, a)) -> c7(MARK(f(y0, y1, a))) MARK(f(f(b, y0, y1), z1, a)) -> c7(MARK(f(b, y0, y1))) MARK(f(f(y0, y1, b), z1, a)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, a)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, a)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, a)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, a)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, a)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, a)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(b, y0, y1))) -> c8(MARK(f(b, y0, y1))) MARK(f(b, z0, f(y0, y1, b))) -> c8(MARK(f(y0, y1, b))) MARK(f(b, z0, f(y0, y1, f(y2, y3, y4)))) -> c8(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, f(y4, y5, y6))))) -> c8(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(b, z0, f(y0, y1, f(y2, y3, c)))) -> c8(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, a)))) -> c8(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, b)))) -> c8(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(b, z0, f(y0, y1, f(f(y2, y3, y4), y5, y6)))) -> c8(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(b, z0, f(y0, y1, f(c, y2, y3)))) -> c8(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(a, y2, y3)))) -> c8(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(b, y2, y3)))) -> c8(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, f(y4, y5, y6)))) -> c8(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(b, z0, f(c, y0, f(y1, y2, y3)))) -> c8(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(a, y0, f(y1, y2, y3)))) -> c8(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, c))) -> c8(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(b, z0, f(y0, y1, c))) -> c8(MARK(f(y0, y1, c))) MARK(f(b, z0, f(c, y0, c))) -> c8(MARK(f(c, y0, c))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, y6))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(b, z0, f(f(y0, y1, c), y2, y3))) -> c8(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(b, z0, f(f(y0, y1, a), y2, y3))) -> c8(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(b, z0, f(f(y0, y1, b), y2, y3))) -> c8(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, y6))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(b, z0, f(f(c, y0, y1), y2, y3))) -> c8(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(b, z0, f(f(a, y0, y1), y2, y3))) -> c8(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(b, z0, f(f(b, y0, y1), y2, y3))) -> c8(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(b, z0, f(f(y0, y1, y2), y3, a))) -> c8(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(b, z0, f(f(y0, y1, y2), y3, b))) -> c8(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(b, z0, f(f(y0, y1, y2), y3, y4))) -> c8(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(b, z0, f(c, y0, y1))) -> c8(MARK(f(c, y0, y1))) MARK(f(b, z0, f(b, y0, f(y1, y2, y3)))) -> c8(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, a), y2, a))) -> c8(MARK(f(f(y0, y1, a), y2, a))) MARK(f(b, z0, f(f(b, y0, y1), y2, a))) -> c8(MARK(f(f(b, y0, y1), y2, a))) MARK(f(b, z0, f(f(y0, y1, b), y2, a))) -> c8(MARK(f(f(y0, y1, b), y2, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, c)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, a)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, b)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) -> c8(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(c, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(a, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(b, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(b, z0, f(f(c, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(a, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, c), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(b, z0, f(f(y0, y1, c), y2, a))) -> c8(MARK(f(f(y0, y1, c), y2, a))) MARK(f(b, z0, f(f(c, y0, c), y1, a))) -> c8(MARK(f(f(c, y0, c), y1, a))) MARK(f(b, z0, f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) -> c8(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(y0, y1, c), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, a), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, b), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) -> c8(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(c, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(a, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(b, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, a), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, b), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(b, z0, f(f(c, y0, y1), y2, a))) -> c8(MARK(f(f(c, y0, y1), y2, a))) MARK(f(b, z0, f(f(b, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(y0, y1, b), z1, b)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, b)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, b)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, b)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, b)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, b)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, c)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, c)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, c)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, c)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(f(y0, y1, b), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, b))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, b))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, b))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, b))) MARK(f(f(f(y0, y1, c), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, b))) MARK(f(f(f(c, y0, c), y1, b), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, b))) MARK(f(f(f(c, y0, y1), y2, b), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, b))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, a), y3, b))) MARK(f(f(f(f(b, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, b), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, c), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, a), y3, b))) MARK(f(f(f(f(c, y0, c), y1, a), y2, b), z1, c)) -> c7(MARK(f(f(f(c, y0, c), y1, a), y2, b))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b))) MARK(f(f(f(f(c, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(b, y0, f(b, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, b)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, b)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, c)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, c)), y3, b))) MARK(f(f(f(b, y0, f(c, y1, c)), y2, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, c)), y2, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b))) MARK(f(f(f(b, y0, f(c, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c7_2, c7_1, c8_2, c8_1, c1_1, c2_1 ---------------------------------------- (179) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(f(x0, x1, c)) -> c7(MARK(x0)) by MARK(f(f(y0, y1, f(y2, y3, y4)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, c)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, c)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, c)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, c)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(f(y0, y1, b), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, b))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, b))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, b))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, b))) MARK(f(f(f(y0, y1, c), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, b))) MARK(f(f(f(c, y0, c), y1, b), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, b))) MARK(f(f(f(c, y0, y1), y2, b), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, b))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, a), y3, b))) MARK(f(f(f(f(b, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, b), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, c), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, a), y3, b))) MARK(f(f(f(f(c, y0, c), y1, a), y2, b), z1, c)) -> c7(MARK(f(f(f(c, y0, c), y1, a), y2, b))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b))) MARK(f(f(f(f(c, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(b, y0, f(b, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, b)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, b)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, c)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, c)), y3, b))) MARK(f(f(f(b, y0, f(c, y1, c)), y2, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, c)), y2, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b))) MARK(f(f(f(b, y0, f(c, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, c))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, c))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, c))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, c))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, c))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, c))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, c))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, c))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, c))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, c))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, c))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, c))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, c))) MARK(f(f(f(y0, y1, c), y2, c), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, c))) MARK(f(f(f(c, y0, c), y1, c), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, c))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, c))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, c))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, c))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, c))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, c))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, c))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, c))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, c))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, c))) MARK(f(f(f(c, y0, y1), y2, c), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, c))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, c))) MARK(f(f(f(f(y0, y1, a), y2, a), y3, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, a), y3, c))) MARK(f(f(f(f(b, y0, y1), y2, a), y3, c), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, a), y3, c))) MARK(f(f(f(f(y0, y1, b), y2, a), y3, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, a), y3, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, c))) MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, c))) MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, c))) MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, c), y2, a), y3, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, a), y3, c))) MARK(f(f(f(f(c, y0, c), y1, a), y2, c), z1, c)) -> c7(MARK(f(f(f(c, y0, c), y1, a), y2, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, c))) MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, c))) MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, c))) MARK(f(f(f(f(c, y0, y1), y2, a), y3, c), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, a), y3, c))) MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, c))) MARK(f(f(f(b, y0, f(b, y1, y2)), y3, c), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, y2)), y3, c))) MARK(f(f(f(b, y0, f(y1, y2, b)), y3, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, b)), y3, c))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, c))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, c))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, c))) MARK(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, c))) MARK(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, c)), y3, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, c)), y3, c))) MARK(f(f(f(b, y0, f(c, y1, c)), y2, c), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, c)), y2, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, c))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, c))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, c))) MARK(f(f(f(b, y0, f(c, y1, y2)), y3, c), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, y2)), y3, c))) MARK(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, c))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, c))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, c))) MARK(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, c))) MARK(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, c))) MARK(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, c))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, c))) MARK(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(f(y0, y1, b), y2, b), y3, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, b), y3, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b), y8, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b), y8, c))) MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b), y8, c))) MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, c), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, c), y2, b), y3, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, b), y3, c))) MARK(f(f(f(f(c, y0, c), y1, b), y2, c), z1, c)) -> c7(MARK(f(f(f(c, y0, c), y1, b), y2, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b), y8, c))) MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b), y8, c))) MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(a, y0, y1), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, a), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, b), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, b), y6, c))) MARK(f(f(f(f(c, y0, y1), y2, b), y3, c), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, b), y3, c))) MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, a), y2, a), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, a), y3, b), y4, c))) MARK(f(f(f(f(f(b, y0, y1), y2, a), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, a), y3, b), y4, c))) MARK(f(f(f(f(f(y0, y1, b), y2, a), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, a), y3, b), y4, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b), y7, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b), y9, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b), y9, c))) MARK(f(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b), y9, c))) MARK(f(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, c), y2, a), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, a), y3, b), y4, c))) MARK(f(f(f(f(f(c, y0, c), y1, a), y2, b), y3, c), z1, c)) -> c7(MARK(f(f(f(f(c, y0, c), y1, a), y2, b), y3, c))) MARK(f(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b), y9, c))) MARK(f(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b), y9, c))) MARK(f(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b), y7, c))) MARK(f(f(f(f(f(c, y0, y1), y2, a), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, a), y3, b), y4, c))) MARK(f(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(b, y1, y2)), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(b, y1, y2)), y3, b), y4, c))) MARK(f(f(f(f(b, y0, f(y1, y2, b)), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, b)), y3, b), y4, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b), y9, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b), y9, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b), y9, c))) MARK(f(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, c)), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, c)), y3, b), y4, c))) MARK(f(f(f(f(b, y0, f(c, y1, c)), y2, b), y3, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(c, y1, c)), y2, b), y3, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b), y9, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b), y9, c))) MARK(f(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(c, y1, y2)), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(c, y1, y2)), y3, b), y4, c))) MARK(f(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b), y5, c))) MARK(f(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b), y5, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b), y5, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b), y8, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b), y10, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b), y10, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b), y10, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b), y10, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b), y10, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b), y10, c))) MARK(f(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b), y5, c))) MARK(f(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b), y4, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b), y10, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b), y10, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b), y10, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b), y10, c))) MARK(f(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b), y8, c))) MARK(f(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b), y5, c))) MARK(f(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c))) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__f(a, b, z0) -> a__f(mark(z0), z0, mark(z0)) a__f(z0, z1, z2) -> f(z0, z1, z2) a__c -> a a__c -> b a__c -> c mark(f(z0, z1, z2)) -> a__f(mark(z0), z1, mark(z2)) mark(c) -> a__c mark(a) -> a mark(b) -> b Tuples: MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(x0, x1, c)) -> c7(MARK(x0)) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) MARK(f(f(y0, y1, a), z1, a)) -> c7(MARK(f(y0, y1, a))) MARK(f(f(b, y0, y1), z1, a)) -> c7(MARK(f(b, y0, y1))) MARK(f(f(y0, y1, b), z1, a)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, a)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, a)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, a)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, a)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, a)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, a)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(b, y0, y1))) -> c8(MARK(f(b, y0, y1))) MARK(f(b, z0, f(y0, y1, b))) -> c8(MARK(f(y0, y1, b))) MARK(f(b, z0, f(y0, y1, f(y2, y3, y4)))) -> c8(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, f(y4, y5, y6))))) -> c8(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(b, z0, f(y0, y1, f(y2, y3, c)))) -> c8(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, a)))) -> c8(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, b)))) -> c8(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(b, z0, f(y0, y1, f(f(y2, y3, y4), y5, y6)))) -> c8(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(b, z0, f(y0, y1, f(c, y2, y3)))) -> c8(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(a, y2, y3)))) -> c8(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(b, y2, y3)))) -> c8(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, f(y4, y5, y6)))) -> c8(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(b, z0, f(c, y0, f(y1, y2, y3)))) -> c8(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(a, y0, f(y1, y2, y3)))) -> c8(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, c))) -> c8(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(b, z0, f(y0, y1, c))) -> c8(MARK(f(y0, y1, c))) MARK(f(b, z0, f(c, y0, c))) -> c8(MARK(f(c, y0, c))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, y6))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(b, z0, f(f(y0, y1, c), y2, y3))) -> c8(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(b, z0, f(f(y0, y1, a), y2, y3))) -> c8(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(b, z0, f(f(y0, y1, b), y2, y3))) -> c8(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, y6))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(b, z0, f(f(c, y0, y1), y2, y3))) -> c8(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(b, z0, f(f(a, y0, y1), y2, y3))) -> c8(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(b, z0, f(f(b, y0, y1), y2, y3))) -> c8(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(b, z0, f(f(y0, y1, y2), y3, a))) -> c8(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(b, z0, f(f(y0, y1, y2), y3, b))) -> c8(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(b, z0, f(f(y0, y1, y2), y3, y4))) -> c8(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(b, z0, f(c, y0, y1))) -> c8(MARK(f(c, y0, y1))) MARK(f(b, z0, f(b, y0, f(y1, y2, y3)))) -> c8(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, a), y2, a))) -> c8(MARK(f(f(y0, y1, a), y2, a))) MARK(f(b, z0, f(f(b, y0, y1), y2, a))) -> c8(MARK(f(f(b, y0, y1), y2, a))) MARK(f(b, z0, f(f(y0, y1, b), y2, a))) -> c8(MARK(f(f(y0, y1, b), y2, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, c)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, a)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, b)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) -> c8(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(c, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(a, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(b, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(b, z0, f(f(c, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(a, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, c), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(b, z0, f(f(y0, y1, c), y2, a))) -> c8(MARK(f(f(y0, y1, c), y2, a))) MARK(f(b, z0, f(f(c, y0, c), y1, a))) -> c8(MARK(f(f(c, y0, c), y1, a))) MARK(f(b, z0, f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) -> c8(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(y0, y1, c), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, a), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, b), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) -> c8(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(c, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(a, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(b, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, a), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, b), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(b, z0, f(f(c, y0, y1), y2, a))) -> c8(MARK(f(f(c, y0, y1), y2, a))) MARK(f(b, z0, f(f(b, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(y0, y1, b), z1, b)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, b)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, b)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, b)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, b)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, b)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, c)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, c)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, c)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, c)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(f(y0, y1, b), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, b))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, b))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, b))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, b))) MARK(f(f(f(y0, y1, c), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, b))) MARK(f(f(f(c, y0, c), y1, b), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, b))) MARK(f(f(f(c, y0, y1), y2, b), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, b))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, a), y3, b))) MARK(f(f(f(f(b, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, b), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, c), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, a), y3, b))) MARK(f(f(f(f(c, y0, c), y1, a), y2, b), z1, c)) -> c7(MARK(f(f(f(c, y0, c), y1, a), y2, b))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b))) MARK(f(f(f(f(c, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(b, y0, f(b, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, b)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, b)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, c)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, c)), y3, b))) MARK(f(f(f(b, y0, f(c, y1, c)), y2, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, c)), y2, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b))) MARK(f(f(f(b, y0, f(c, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, c))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, c))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, c))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, c))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, c))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, c))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, c))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, c))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, c))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, c))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, c))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, c))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, c))) MARK(f(f(f(y0, y1, c), y2, c), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, c))) MARK(f(f(f(c, y0, c), y1, c), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, c))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, c))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, c))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, c))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, c))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, c))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, c))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, c))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, c))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, c))) MARK(f(f(f(c, y0, y1), y2, c), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, c))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, c))) MARK(f(f(f(f(y0, y1, a), y2, a), y3, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, a), y3, c))) MARK(f(f(f(f(b, y0, y1), y2, a), y3, c), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, a), y3, c))) MARK(f(f(f(f(y0, y1, b), y2, a), y3, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, a), y3, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, c))) MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, c))) MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, c))) MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, c))) MARK(f(f(f(f(y0, y1, c), y2, a), y3, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, a), y3, c))) MARK(f(f(f(f(c, y0, c), y1, a), y2, c), z1, c)) -> c7(MARK(f(f(f(c, y0, c), y1, a), y2, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, c))) MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, c))) MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, c))) MARK(f(f(f(f(c, y0, y1), y2, a), y3, c), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, a), y3, c))) MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, c))) MARK(f(f(f(b, y0, f(b, y1, y2)), y3, c), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, y2)), y3, c))) MARK(f(f(f(b, y0, f(y1, y2, b)), y3, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, b)), y3, c))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, c))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, c))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, c))) MARK(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, c))) MARK(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, c))) MARK(f(f(f(b, y0, f(y1, y2, c)), y3, c), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, c)), y3, c))) MARK(f(f(f(b, y0, f(c, y1, c)), y2, c), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, c)), y2, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, c))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, c))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, c))) MARK(f(f(f(b, y0, f(c, y1, y2)), y3, c), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, y2)), y3, c))) MARK(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, c), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, c))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, c))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, c))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, c))) MARK(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, c))) MARK(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, c))) MARK(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, c))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, c))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, c))) MARK(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, c), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, c))) MARK(f(f(f(f(y0, y1, b), y2, b), y3, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, b), y3, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b), y8, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b), y8, c))) MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b), y8, c))) MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, c), y4, b), y5, c))) MARK(f(f(f(f(y0, y1, c), y2, b), y3, c), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, b), y3, c))) MARK(f(f(f(f(c, y0, c), y1, b), y2, c), z1, c)) -> c7(MARK(f(f(f(c, y0, c), y1, b), y2, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b), y8, c))) MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b), y8, c))) MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(a, y0, y1), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, y3), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, a), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, b), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, b), y6, c))) MARK(f(f(f(f(c, y0, y1), y2, b), y3, c), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, b), y3, c))) MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, b), y5, c))) MARK(f(f(f(f(f(y0, y1, a), y2, a), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, a), y3, b), y4, c))) MARK(f(f(f(f(f(b, y0, y1), y2, a), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, a), y3, b), y4, c))) MARK(f(f(f(f(f(y0, y1, b), y2, a), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, a), y3, b), y4, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b), y7, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b), y9, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b), y9, c))) MARK(f(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b), y9, c))) MARK(f(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(y0, y1, c), y2, a), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, a), y3, b), y4, c))) MARK(f(f(f(f(f(c, y0, c), y1, a), y2, b), y3, c), z1, c)) -> c7(MARK(f(f(f(f(c, y0, c), y1, a), y2, b), y3, c))) MARK(f(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b), y9, c))) MARK(f(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b), y9, c))) MARK(f(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b), y6, c))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b), y7, c))) MARK(f(f(f(f(f(c, y0, y1), y2, a), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, a), y3, b), y4, c))) MARK(f(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(b, y1, y2)), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(b, y1, y2)), y3, b), y4, c))) MARK(f(f(f(f(b, y0, f(y1, y2, b)), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, b)), y3, b), y4, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b), y9, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b), y9, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b), y9, c))) MARK(f(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(y1, y2, c)), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, c)), y3, b), y4, c))) MARK(f(f(f(f(b, y0, f(c, y1, c)), y2, b), y3, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(c, y1, c)), y2, b), y3, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b), y9, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b), y9, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b), y9, c))) MARK(f(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(c, y1, y2)), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(c, y1, y2)), y3, b), y4, c))) MARK(f(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b), y6, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b), y6, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b), y5, c))) MARK(f(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b), y5, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b), y5, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b), y8, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b), y10, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b), y10, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b), y10, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b), y10, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b), y10, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b), y10, c))) MARK(f(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b), y5, c))) MARK(f(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b), y4, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b), y4, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b), y10, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b), y10, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b), y10, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b), y10, c))) MARK(f(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b), y7, c))) MARK(f(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b), y8, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b), y8, c))) MARK(f(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b), y5, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b), y5, c))) MARK(f(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c), z1, c)) -> c7(MARK(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b), y7, c))) S tuples: MARK(f(x0, x1, f(x2, z1, x4))) -> c7(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(x0)) MARK(f(x0, x1, f(x2, x3, c))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, a))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(x0)) MARK(f(x0, x1, f(x2, x3, b))) -> c7(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(x0)) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(c, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(a, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(x0)) MARK(f(x0, x1, f(b, x3, x4))) -> c7(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(x0)) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(z0, z1, z2))) MARK(f(c, x1, f(x2, x3, x4))) -> c7(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(a, x1, f(x2, x3, x4))) -> c7(A__F(a, x1, a__f(mark(x2), x3, mark(x4)))) MARK(f(f(z0, z1, z2), x1, c)) -> c7(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__c), MARK(f(z0, z1, z2))) MARK(f(c, x1, c)) -> c7(A__F(a__c, x1, a__c)) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(f(x0, x1, f(z0, z1, z2)))) MARK(f(f(x0, x1, c), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(f(x0, x1, c))) MARK(f(f(x0, x1, a), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(f(x0, x1, a))) MARK(f(f(x0, x1, b), x3, x4)) -> c7(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(f(x0, x1, b))) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c7(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(f(f(z0, z1, z2), x1, x2))) MARK(f(f(c, x1, x2), x3, x4)) -> c7(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(f(c, x1, x2))) MARK(f(f(a, x1, x2), x3, x4)) -> c7(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(f(a, x1, x2))) MARK(f(f(b, x1, x2), x3, x4)) -> c7(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(f(b, x1, x2))) MARK(f(f(x0, x1, x2), x3, a)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, x1, x2), x3, b)) -> c7(MARK(f(x0, x1, x2))) MARK(f(f(x0, z1, x2), x3, x4)) -> c7(MARK(f(x0, z1, x2))) MARK(f(c, x0, x1)) -> c7(A__F(a, x0, mark(x1))) MARK(f(x0, x1, f(x2, z1, x4))) -> c8(A__F(mark(x0), x1, f(mark(x2), z1, mark(x4))), MARK(f(x2, z1, x4))) MARK(f(x0, x1, f(x2, x3, f(z0, z1, z2)))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__f(mark(z0), z1, mark(z2)))), MARK(f(x2, x3, f(z0, z1, z2)))) MARK(f(x0, x1, f(x2, x3, c))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a__c)), MARK(f(x2, x3, c))) MARK(f(x0, x1, f(x2, x3, a))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, a)), MARK(f(x2, x3, a))) MARK(f(x0, x1, f(x2, x3, b))) -> c8(A__F(mark(x0), x1, a__f(mark(x2), x3, b)), MARK(f(x2, x3, b))) MARK(f(x0, x1, f(f(z0, z1, z2), x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__f(mark(z0), z1, mark(z2)), x3, mark(x4))), MARK(f(f(z0, z1, z2), x3, x4))) MARK(f(x0, x1, f(c, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a__c, x3, mark(x4))), MARK(f(c, x3, x4))) MARK(f(x0, x1, f(a, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(a, x3, mark(x4))), MARK(f(a, x3, x4))) MARK(f(x0, x1, f(b, x3, x4))) -> c8(A__F(mark(x0), x1, a__f(b, x3, mark(x4))), MARK(f(b, x3, x4))) MARK(f(f(z0, z1, z2), x1, f(x2, x3, x4))) -> c8(A__F(a__f(mark(z0), z1, mark(z2)), x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(c, x1, f(x2, x3, x4))) -> c8(A__F(a__c, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(a, x1, f(x2, x3, x4))) -> c8(A__F(a, x1, a__f(mark(x2), x3, mark(x4))), MARK(f(x2, x3, x4))) MARK(f(b, x1, f(x2, x3, x4))) -> c8(MARK(f(x2, x3, x4))) MARK(f(f(x0, x1, f(z0, z1, z2)), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__f(mark(z0), z1, mark(z2))), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, c), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a__c), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, a), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, a), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, b), x3, x4)) -> c8(A__F(a__f(mark(x0), x1, b), x3, mark(x4)), MARK(x4)) MARK(f(f(f(z0, z1, z2), x1, x2), x3, x4)) -> c8(A__F(a__f(a__f(mark(z0), z1, mark(z2)), x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(c, x1, x2), x3, x4)) -> c8(A__F(a__f(a__c, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(a, x1, x2), x3, x4)) -> c8(A__F(a__f(a, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(b, x1, x2), x3, x4)) -> c8(A__F(a__f(b, x1, mark(x2)), x3, mark(x4)), MARK(x4)) MARK(f(f(x0, x1, x2), x3, c)) -> c8(A__F(a__f(mark(x0), x1, mark(x2)), x3, a__c)) MARK(f(f(x0, z1, x2), x3, x4)) -> c8(MARK(x4)) MARK(f(c, x0, x1)) -> c8(A__F(a, x0, mark(x1)), MARK(x1)) MARK(f(c, x0, c)) -> c8(A__F(a__c, x0, a__c)) MARK(f(c, x0, x1)) -> c8(MARK(x1)) A__F(a, b, f(z0, z1, a)) -> c1(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c1(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c1(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c1(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c1(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c1(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c1(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c1(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c1(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c1(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c1(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c1(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c1(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c1(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c1(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c1(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c1(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c1(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c1(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c1(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c1(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c1(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c1(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c1(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c1(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c1(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c1(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c1(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c1(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c1(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c1(MARK(f(b, z1, f(y1, y2, y3)))) A__F(a, b, f(z0, z1, a)) -> c2(MARK(f(z0, z1, a))) A__F(a, b, f(b, z1, z2)) -> c2(MARK(f(b, z1, z2))) A__F(a, b, f(z0, z1, b)) -> c2(MARK(f(z0, z1, b))) A__F(a, b, f(z0, z1, f(y2, y3, y4))) -> c2(MARK(f(z0, z1, f(y2, y3, y4)))) A__F(a, b, f(z0, z1, f(y2, y3, f(y4, y5, y6)))) -> c2(MARK(f(z0, z1, f(y2, y3, f(y4, y5, y6))))) A__F(a, b, f(z0, z1, f(y2, y3, c))) -> c2(MARK(f(z0, z1, f(y2, y3, c)))) A__F(a, b, f(z0, z1, f(y2, y3, a))) -> c2(MARK(f(z0, z1, f(y2, y3, a)))) A__F(a, b, f(z0, z1, f(y2, y3, b))) -> c2(MARK(f(z0, z1, f(y2, y3, b)))) A__F(a, b, f(z0, z1, f(f(y2, y3, y4), y5, y6))) -> c2(MARK(f(z0, z1, f(f(y2, y3, y4), y5, y6)))) A__F(a, b, f(z0, z1, f(c, y2, y3))) -> c2(MARK(f(z0, z1, f(c, y2, y3)))) A__F(a, b, f(z0, z1, f(a, y2, y3))) -> c2(MARK(f(z0, z1, f(a, y2, y3)))) A__F(a, b, f(z0, z1, f(b, y2, y3))) -> c2(MARK(f(z0, z1, f(b, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, f(y4, y5, y6))) -> c2(MARK(f(f(y0, y1, y2), z1, f(y4, y5, y6)))) A__F(a, b, f(c, z1, f(y1, y2, y3))) -> c2(MARK(f(c, z1, f(y1, y2, y3)))) A__F(a, b, f(a, z1, f(y1, y2, y3))) -> c2(MARK(f(a, z1, f(y1, y2, y3)))) A__F(a, b, f(f(y0, y1, y2), z1, c)) -> c2(MARK(f(f(y0, y1, y2), z1, c))) A__F(a, b, f(z0, z1, c)) -> c2(MARK(f(z0, z1, c))) A__F(a, b, f(c, z1, c)) -> c2(MARK(f(c, z1, c))) A__F(a, b, f(f(y0, y1, f(y2, y3, y4)), z1, z2)) -> c2(MARK(f(f(y0, y1, f(y2, y3, y4)), z1, z2))) A__F(a, b, f(f(y0, y1, c), z1, z2)) -> c2(MARK(f(f(y0, y1, c), z1, z2))) A__F(a, b, f(f(y0, y1, a), z1, z2)) -> c2(MARK(f(f(y0, y1, a), z1, z2))) A__F(a, b, f(f(y0, y1, b), z1, z2)) -> c2(MARK(f(f(y0, y1, b), z1, z2))) A__F(a, b, f(f(f(y0, y1, y2), y3, y4), z1, z2)) -> c2(MARK(f(f(f(y0, y1, y2), y3, y4), z1, z2))) A__F(a, b, f(f(c, y0, y1), z1, z2)) -> c2(MARK(f(f(c, y0, y1), z1, z2))) A__F(a, b, f(f(a, y0, y1), z1, z2)) -> c2(MARK(f(f(a, y0, y1), z1, z2))) A__F(a, b, f(f(b, y0, y1), z1, z2)) -> c2(MARK(f(f(b, y0, y1), z1, z2))) A__F(a, b, f(f(y0, y1, y2), z1, a)) -> c2(MARK(f(f(y0, y1, y2), z1, a))) A__F(a, b, f(f(y0, y1, y2), z1, b)) -> c2(MARK(f(f(y0, y1, y2), z1, b))) A__F(a, b, f(f(y0, y1, y2), z1, z2)) -> c2(MARK(f(f(y0, y1, y2), z1, z2))) A__F(a, b, f(c, z1, z2)) -> c2(MARK(f(c, z1, z2))) A__F(a, b, f(b, z1, f(y1, y2, y3))) -> c2(MARK(f(b, z1, f(y1, y2, y3)))) MARK(f(f(y0, y1, a), z1, a)) -> c7(MARK(f(y0, y1, a))) MARK(f(f(b, y0, y1), z1, a)) -> c7(MARK(f(b, y0, y1))) MARK(f(f(y0, y1, b), z1, a)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, a)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, a)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, a)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, a)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, a)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, a)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, a)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, a)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, a)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, a)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, a)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, a)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(b, y0, y1))) -> c8(MARK(f(b, y0, y1))) MARK(f(b, z0, f(y0, y1, b))) -> c8(MARK(f(y0, y1, b))) MARK(f(b, z0, f(y0, y1, f(y2, y3, y4)))) -> c8(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, f(y4, y5, y6))))) -> c8(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(b, z0, f(y0, y1, f(y2, y3, c)))) -> c8(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, a)))) -> c8(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(b, z0, f(y0, y1, f(y2, y3, b)))) -> c8(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(b, z0, f(y0, y1, f(f(y2, y3, y4), y5, y6)))) -> c8(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(b, z0, f(y0, y1, f(c, y2, y3)))) -> c8(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(a, y2, y3)))) -> c8(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(b, z0, f(y0, y1, f(b, y2, y3)))) -> c8(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, f(y4, y5, y6)))) -> c8(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(b, z0, f(c, y0, f(y1, y2, y3)))) -> c8(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(a, y0, f(y1, y2, y3)))) -> c8(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, y2), y3, c))) -> c8(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(b, z0, f(y0, y1, c))) -> c8(MARK(f(y0, y1, c))) MARK(f(b, z0, f(c, y0, c))) -> c8(MARK(f(c, y0, c))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, y6))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(b, z0, f(f(y0, y1, c), y2, y3))) -> c8(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(b, z0, f(f(y0, y1, a), y2, y3))) -> c8(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(b, z0, f(f(y0, y1, b), y2, y3))) -> c8(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, y6))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(b, z0, f(f(c, y0, y1), y2, y3))) -> c8(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(b, z0, f(f(a, y0, y1), y2, y3))) -> c8(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(b, z0, f(f(b, y0, y1), y2, y3))) -> c8(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(b, z0, f(f(y0, y1, y2), y3, a))) -> c8(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(b, z0, f(f(y0, y1, y2), y3, b))) -> c8(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(b, z0, f(f(y0, y1, y2), y3, y4))) -> c8(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(b, z0, f(c, y0, y1))) -> c8(MARK(f(c, y0, y1))) MARK(f(b, z0, f(b, y0, f(y1, y2, y3)))) -> c8(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(b, z0, f(f(y0, y1, a), y2, a))) -> c8(MARK(f(f(y0, y1, a), y2, a))) MARK(f(b, z0, f(f(b, y0, y1), y2, a))) -> c8(MARK(f(f(b, y0, y1), y2, a))) MARK(f(b, z0, f(f(y0, y1, b), y2, a))) -> c8(MARK(f(f(y0, y1, b), y2, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, y4)), y5, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, c)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, a)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(y2, y3, b)), y4, a))) -> c8(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) -> c8(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(b, z0, f(f(y0, y1, f(c, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(a, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(b, z0, f(f(y0, y1, f(b, y2, y3)), y4, a))) -> c8(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(b, z0, f(f(c, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(a, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, c), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(b, z0, f(f(y0, y1, c), y2, a))) -> c8(MARK(f(f(y0, y1, c), y2, a))) MARK(f(b, z0, f(f(c, y0, c), y1, a))) -> c8(MARK(f(f(c, y0, c), y1, a))) MARK(f(b, z0, f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) -> c8(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(y0, y1, c), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, a), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, b), y2, y3), y4, a))) -> c8(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) -> c8(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(b, z0, f(f(f(c, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(a, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(b, y0, y1), y2, y3), y4, a))) -> c8(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, a), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, b), y4, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(b, z0, f(f(f(y0, y1, y2), y3, y4), y5, a))) -> c8(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(b, z0, f(f(c, y0, y1), y2, a))) -> c8(MARK(f(f(c, y0, y1), y2, a))) MARK(f(b, z0, f(f(b, y0, f(y1, y2, y3)), y4, a))) -> c8(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(y0, y1, b), z1, b)) -> c7(MARK(f(y0, y1, b))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, b)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, b)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, b)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, b)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, b)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, b)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, b)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, b)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, b)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, b)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, b)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, b)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, b)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, b)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, b)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, b)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, b)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, b)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(y0, y1, f(y2, y3, y4)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, y4)))) MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, f(y4, y5, y6))))) MARK(f(f(y0, y1, f(y2, y3, c)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, c)))) MARK(f(f(y0, y1, f(y2, y3, a)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, a)))) MARK(f(f(y0, y1, f(y2, y3, b)), z1, c)) -> c7(MARK(f(y0, y1, f(y2, y3, b)))) MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), z1, c)) -> c7(MARK(f(y0, y1, f(f(y2, y3, y4), y5, y6)))) MARK(f(f(y0, y1, f(c, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(c, y2, y3)))) MARK(f(f(y0, y1, f(a, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(a, y2, y3)))) MARK(f(f(y0, y1, f(b, y2, y3)), z1, c)) -> c7(MARK(f(y0, y1, f(b, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, f(y4, y5, y6)))) MARK(f(f(c, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(c, y0, f(y1, y2, y3)))) MARK(f(f(a, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(a, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, y2), y3, c), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, c))) MARK(f(f(y0, y1, c), z1, c)) -> c7(MARK(f(y0, y1, c))) MARK(f(f(c, y0, c), z1, c)) -> c7(MARK(f(c, y0, c))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, y6))) MARK(f(f(f(y0, y1, c), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, y3))) MARK(f(f(f(y0, y1, a), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, y3))) MARK(f(f(f(y0, y1, b), y2, y3), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, y3))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, y6))) MARK(f(f(f(c, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, y3))) MARK(f(f(f(a, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(a, y0, y1), y2, y3))) MARK(f(f(f(b, y0, y1), y2, y3), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, y3))) MARK(f(f(f(y0, y1, y2), y3, a), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, a))) MARK(f(f(f(y0, y1, y2), y3, b), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, b))) MARK(f(f(f(y0, y1, y2), y3, y4), z1, c)) -> c7(MARK(f(f(y0, y1, y2), y3, y4))) MARK(f(f(c, y0, y1), z1, c)) -> c7(MARK(f(c, y0, y1))) MARK(f(f(b, y0, f(y1, y2, y3)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, y3)))) MARK(f(f(f(y0, y1, a), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, a), y2, a))) MARK(f(f(f(b, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(b, y0, y1), y2, a))) MARK(f(f(f(y0, y1, b), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, a))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, a))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, a))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, a))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, a))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, a))) MARK(f(f(f(y0, y1, c), y2, a), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, a))) MARK(f(f(f(c, y0, c), y1, a), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, a))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, a))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, a))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, a))) MARK(f(f(f(c, y0, y1), y2, a), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, a))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, a))) MARK(f(f(b, y0, f(b, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, y2)))) MARK(f(f(b, y0, f(y1, y2, b)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, b)))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, y5))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, c))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, a))))) MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(y3, y4, b))))) MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))))) MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(c, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(a, y3, y4))))) MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, f(b, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))))) MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(a, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, c)))) MARK(f(f(b, y0, f(y1, y2, c)), z1, c)) -> c7(MARK(f(b, y0, f(y1, y2, c)))) MARK(f(f(b, y0, f(c, y1, c)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, c)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, y4)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, y4)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, a)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, b)))) MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, y3), y4, y5)))) MARK(f(f(b, y0, f(c, y1, y2)), z1, c)) -> c7(MARK(f(b, y0, f(c, y1, y2)))) MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), z1, c)) -> c7(MARK(f(b, y0, f(b, y1, f(y2, y3, y4))))) MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, a), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, b), y3, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)))) MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)))) MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(y1, y2, c), y3, a)))) MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, c), y2, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)))) MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)))) MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)))) MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(c, y1, y2), y3, a)))) MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), z1, c)) -> c7(MARK(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)))) MARK(f(f(f(y0, y1, b), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, b), y2, b))) MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, y4)), y5, b))) MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, b))) MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, c)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, a)), y4, b))) MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(y2, y3, b)), y4, b))) MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, b))) MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(c, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(a, y2, y3)), y4, b))) MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(y0, y1, f(b, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, b))) MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(c, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(a, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, c), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, c), y4, b))) MARK(f(f(f(y0, y1, c), y2, b), z1, c)) -> c7(MARK(f(f(y0, y1, c), y2, b))) MARK(f(f(f(c, y0, c), y1, b), z1, c)) -> c7(MARK(f(f(c, y0, c), y1, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, b))) MARK(f(f(f(f(y0, y1, c), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, b), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, y3), y4, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, b))) MARK(f(f(f(f(c, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(a, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(a, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(b, y0, y1), y2, y3), y4, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, y3), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, a), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, a), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, b), y4, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, b), y4, b))) MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, y2), y3, y4), y5, b))) MARK(f(f(f(c, y0, y1), y2, b), z1, c)) -> c7(MARK(f(f(c, y0, y1), y2, b))) MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, y3)), y4, b))) MARK(f(f(f(f(y0, y1, a), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, a), y2, a), y3, b))) MARK(f(f(f(f(b, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(b, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, b), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, b), y2, a), y3, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, y4)), y5, a), y6, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, f(y4, y5, y6))), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, c)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, a)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(y2, y3, b)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(f(y2, y3, y4), y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(c, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(a, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, f(b, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, f(y4, y5, y6)), y7, a), y8, b))) MARK(f(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(c, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(a, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, c), y4, a), y5, b))) MARK(f(f(f(f(y0, y1, c), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(y0, y1, c), y2, a), y3, b))) MARK(f(f(f(f(c, y0, c), y1, a), y2, b), z1, c)) -> c7(MARK(f(f(f(c, y0, c), y1, a), y2, b))) MARK(f(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, f(y2, y3, y4)), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, c), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, a), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, b), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b), z1, c)) -> c7(MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, y6), y7, a), y8, b))) MARK(f(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(c, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(a, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(b, y0, y1), y2, y3), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, a), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, b), y4, a), y5, b))) MARK(f(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b), z1, c)) -> c7(MARK(f(f(f(f(y0, y1, y2), y3, y4), y5, a), y6, b))) MARK(f(f(f(f(c, y0, y1), y2, a), y3, b), z1, c)) -> c7(MARK(f(f(f(c, y0, y1), y2, a), y3, b))) MARK(f(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b), z1, c)) -> c7(MARK(f(f(f(b, y0, f(y1, y2, y3)), y4, a), y5, b))) MARK(f(f(f(b, y0, f(b, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, b)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, b)), y3, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, y5))), y6, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, f(y5, y6, y7)))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, c))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, a))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(y3, y4, b))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(f(y3, y4, y5), y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(c, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(a, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, f(b, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, f(y5, y6, y7))), y8, b))) MARK(f(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(a, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, c)), y5, b))) MARK(f(f(f(b, y0, f(y1, y2, c)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(y1, y2, c)), y3, b))) MARK(f(f(f(b, y0, f(c, y1, c)), y2, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, c)), y2, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, y7)), y8, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, y4)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, a)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, b)), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, y3), y4, y5)), y6, b))) MARK(f(f(f(b, y0, f(c, y1, y2)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(c, y1, y2)), y3, b))) MARK(f(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b), z1, c)) -> c7(MARK(f(f(b, y0, f(b, y1, f(y2, y3, y4))), y5, b))) MARK(f(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, a), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, b), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, y5)), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, f(y5, y6, y7))), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, c)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, a)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(y3, y4, b)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(f(y3, y4, y5), y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(c, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(a, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, f(b, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, f(y5, y6, y7)), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(a, y1, f(y2, y3, y4)), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, c), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(y1, y2, c), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, c), y2, a)), y3, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, f(y3, y4, y5)), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, c), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, a), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, b), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(f(y1, y2, y3), y4, y5), y6, y7), y8, a)), y9, b))) MARK(f(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(c, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(a, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(b, y1, y2), y3, y4), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, a), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, b), y5, a)), y6, b))) MARK(f(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(f(y1, y2, y3), y4, y5), y6, a)), y7, b))) MARK(f(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(c, y1, y2), y3, a)), y4, b))) MARK(f(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b), z1, c)) -> c7(MARK(f(f(b, y0, f(f(b, y1, f(y2, y3, y4)), y5, a)), y6, b))) K tuples:none Defined Rule Symbols: a__f_3, a__c, mark_1 Defined Pair Symbols: MARK_1, A__F_3 Compound Symbols: c7_2, c7_1, c8_2, c8_1, c1_1, c2_1